Applied Analysis Research Papers - Academia.edu (original) (raw)
2025, Journal of Applied Analysis
In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic... more
In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic summability methods
2025, Journal of Applied Analysis
We study a particular class of transition kernels that stems from differentiating Markov kernels in the weak sense. Sufficient conditions are established for this type of kernels to admit a Jordan-type decomposition. The decomposition is... more
We study a particular class of transition kernels that stems from differentiating Markov kernels in the weak sense. Sufficient conditions are established for this type of kernels to admit a Jordan-type decomposition. The decomposition is explicitly constructed.
2025
A. This work presents a comprehensive analysis of integral stability for impulsive dynamic equations on time scales using the comparison principle framework. We first establish a comparison theorem, which provides a rigorous basis for... more
A. This work presents a comprehensive analysis of integral stability for impulsive dynamic equations on time scales using the comparison principle framework. We first establish a comparison theorem, which provides a rigorous basis for comparing the behavior of the main complex system to that of a simpler system of lower order known as the comparison system, whose qualitative properties are easier to ascertain. Building on this result, we derive an integral stability theorem, offering sufficient conditions for integral stability in terms of the properties of the comparison system. Our approach leverages the vector Lyapunov functions and comparison equations to ensure the cumulative effect of impulses and system dynamics remains bounded. The theoretical findings are validated through an illustrative example, demonstrating the applicability of the proposed framework to systems with mixed continuous-discrete dynamics and impulsive effects.
2025, Journal of Applied Analysis
Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, for example, wireless sensor networks. In this paper, we discuss a generalization of fusion... more
Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, for example, wireless sensor networks. In this paper, we discuss a generalization of fusion frames, K-fusion frames. K-fusion frames provide decompositions of a Hilbert space into atomic subspaces with respect to a bounded linear operator. This article studies various kinds of properties of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.
2025
In this paper a stiffness control strategy based on the fuzzy mapped nonlinear terms of the robot manipulator dynamic model is proposed. The proposed stiffness controller is evaluated on a research robot manipulator performing a task in... more
In this paper a stiffness control strategy based on the fuzzy mapped nonlinear terms of the robot manipulator dynamic model is proposed. The proposed stiffness controller is evaluated on a research robot manipulator performing a task in the operational space. Tests attempted to achieve fast motion with reasonable accuracy associated with lower computational load compared to the non-fuzzy approach. The stability analysis is presented to conclude about the mapping error influence and to obtain precondition criteria for the gains adjustment to face the trajectory tracking problem. Simulation results that supported the implementation are presented, followed by experiments and results obtained. These tests are conducted on a robot manipulator with SCARA configuration to illustrate the feasibility of this strategy.
2025, Journal of Applied Analysis
We establish L q convergence for Hamiltonian Monte Carlo algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ q < ∞ and weakly... more
We establish L q convergence for Hamiltonian Monte Carlo algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ q < ∞ and weakly for 1 < q < 2) to the desired target distribution.
2025, arXiv (Cornell University)
We establish L q convergence for Hamiltonian Monte Carlo algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ q < ∞ and weakly... more
We establish L q convergence for Hamiltonian Monte Carlo algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ q < ∞ and weakly for 1 < q < 2) to the desired target distribution.
2025
The goal of this project is to study approximation results for multivalued continuous and *-nonexpansive maps on both compact convex and noncompact convex subsets of metrizable topological vector spaces and hyperconvex spaces. Our main... more
The goal of this project is to study approximation results for multivalued continuous and *-nonexpansive maps on both compact convex and noncompact convex subsets of metrizable topological vector spaces and hyperconvex spaces. Our main tool will be the well known Ky Fan's intersection lemma. We will mainly focus on deterministic and random versions of Fan's approximation theorem for multivalued continuous and *-nonexpansive maps on a metrizable topological vector space. As applications of our results we aniticpate that some well known theorems in approximation theory would follow as corollaries to our results, thus broaderning the scope of approximation theory.
2025, Journal of Applied Analysis
A functional equation related to a problem of linear dependence of iterates is considered.
2025
In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation f (k) + Ak−1f (k−1) + . . .+ A2f ′′ + (D1(z) +A1(z)e )f ′ + (D0(z) +A0(z)e )f = F (k > 2), where a, b are complex... more
In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation f (k) + Ak−1f (k−1) + . . .+ A2f ′′ + (D1(z) +A1(z)e )f ′ + (D0(z) +A0(z)e )f = F (k > 2), where a, b are complex constants that satisfy ab(a− b) 6= 0 and Aj(z) (j = 0, 1, . . . , k − 1), Dj(z) (j = 0, 1), F (z) are entire functions with max{(Aj) (j = 0, 1, . . . , k − 1), (Dj) (j = 0, 1)} < 1. We also investigate the relationship between small functions and the solutions of the above equation.
2025
In this article, we study the relationship between the derivatives of the solutions to the differential equation f (k) +Ak−1f (k−1) + · · ·+A0f = 0 and entire functions of finite order.
2025
In this article, we give sufficiently conditions for the solutions and the differential polynomials generated by second-order differential equations to have the same properties of growth and oscillation. Also answer to the question posed... more
In this article, we give sufficiently conditions for the solutions and the differential polynomials generated by second-order differential equations to have the same properties of growth and oscillation. Also answer to the question posed by Cao [6] for the second-order linear differential equations in the unit disc.
2025, International Journal of Open Problems in Computer Science and Mathematics
In the paper, the authors introduce a new concept "(β, α)-logarithmically convex functions in the first and second sense" and establish Hermite-Hadamard type integral inequalities for these convexities.
2025, arXiv (Cornell University)
Characterizations of paracompact finite C-spaces via continuous selections avoiding Z σ -sets are given. We apply these results to obtain some properties of finite C-spaces. Factorization theorems and a completion theorem for finite... more
Characterizations of paracompact finite C-spaces via continuous selections avoiding Z σ -sets are given. We apply these results to obtain some properties of finite C-spaces. Factorization theorems and a completion theorem for finite C-spaces are also proved.
2025, Journal of Applied Analysis
Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single... more
Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type dual multiobjective control problems are formulated and usual duality results are established under invexity/generalized invexity, relating properly efficient solutions of the primal and dual problems. Wolfe and Mond-Weir type dual multiobjective control problems with free boundary conditions are also presented.
2025, Journal of Optimization Theory and Applications
A quasivariational inequality is a variational inequality in which the constraint set depends on the variable. Based on fixed point techniques, we prove various existence results under weak assumptions on the set-valued operator defining... more
A quasivariational inequality is a variational inequality in which the constraint set depends on the variable. Based on fixed point techniques, we prove various existence results under weak assumptions on the set-valued operator defining the quasivariational inequality, namely quasimonotonicity and lower or upper signcontinuity. Applications to quasi-optimization and traffic network are also considered.
2025, Journal of Global Optimization
We investigate continuity properties (closedness and lower semicontinuity) of the solution map of a quasivariational inequality which is subjet to perturbations. Perturbations are here considered both on the set-valued operator and on the... more
We investigate continuity properties (closedness and lower semicontinuity) of the solution map of a quasivariational inequality which is subjet to perturbations. Perturbations are here considered both on the set-valued operator and on the constraint map defining the quasivariational inequality. Two concepts of solution map will be considered.
2025, Journal of Applied Analysis
We apply a fixed point theorem to prove that there exists a unique derivation close to an approximately generalized derivation in Lie C *-algebras. Also, we prove the hyperstability of generalized derivations. In other words, we find some... more
We apply a fixed point theorem to prove that there exists a unique derivation close to an approximately generalized derivation in Lie C *-algebras. Also, we prove the hyperstability of generalized derivations. In other words, we find some conditions under which an approximately generalized derivation becomes a derivation.
2025
In this paper, we introduce a new subclass of meromorphic multivalent functions associated with Wright generalized hypergeometric function and obtain new results for this class by the application of Briot-Bouquet differential subordination.
2024, Journal of Applied Analysis
Let K be a closed convex cone in a real Banach space, H : K → cc ( K ) {H\colon K\to\operatorname{cc}(K)} a continuous sublinear correspondence with nonempty, convex and compact values in K, and let f : ℝ → ℝ... more
Let K be a closed convex cone in a real Banach space, H : K → cc ( K ) {H\colon K\to\operatorname{cc}(K)} a continuous sublinear correspondence with nonempty, convex and compact values in K, and let f : ℝ → ℝ {f\colon\mathbb{R}\to\mathbb{R}} be defined by f ( t ) = ∑ n = 0 ∞ a n t n {f(t)=\sum_{n=0}^{\infty}a_{n}t^{n}} , where t ∈ ℝ {t\in\mathbb{R}} , a n ≥ 0 {a_{n}\geq 0} , n ∈ ℕ {n\in\mathbb{N}} . We show that the correspondence F t ( x ) : = ∑ n = 0 ∞ a n t n H n ( x ) , ( x ∈ K ) {F^{t}(x)\mathrel{\mathop{:}}=\sum_{n=0}^{\infty}a_{n}t^{n}H^{n}(x),(x\in K)} is continuous and sublinear for every t ≥ 0 {t\geq 0} and F t ∘ F s ( x ) ⊆ ∑ n = 0 ∞ c n H n ( x ) {F^{t}\circ F^{s}(x)\subseteq\sum_{n=0}^{\infty}c_{n}H^{n}(x)} , x ∈ K {x\in K} , where c n = ∑ k = 0 n a k a n - k t k s n - k {c_{n}=\sum_{k=0}^{n}a_{k}a_{n-k}t^{k}s^{n-k}} , t , s ≥ 0 {t,s\geq 0} .
2024, Journal of Taibah University for Science
In this paper, a new logarithmic penalty function method is used for solving nonlinear multiobjective fractional programming problems (MOFPP) involving invex objectives and constraints functions with respect to the same function η. This... more
In this paper, a new logarithmic penalty function method is used for solving nonlinear multiobjective fractional programming problems (MOFPP) involving invex objectives and constraints functions with respect to the same function η. This approach is implemented by modifying fractional objective function to α-invex function, no parameterizations to multi-objective fractional programming problem are required. Furthermore, the constrained multi-objective FPP has been converted to a sequence of unconstrained optimization problems by adding a new logarithmic penalty function to each objective function.
2024
In this paper, we firstly establish generalized weighted Montgomery identity for double integrals. Then, some generalized weightedČebysev and Ostrowski type inequalities for double integrals are given.
2024, Journal of Applied Analysis
In this paper, we establish fractional Ostrowski’s inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality.
2024, IJMTT
Fractional calculus broadens the scope of conventional calculus by introducing derivatives and integrals of nonwhole number orders. This mathematical field expands the ideas of differentiation and integration beyond integer values,... more
Fractional calculus broadens the scope of conventional calculus by introducing derivatives and integrals of nonwhole number orders. This mathematical field expands the ideas of differentiation and integration beyond integer values, offering versatile methods for describing intricate processes across diverse scientific and engineering disciplines. The abstract explores the fundamental definitions, properties, and applications of fractional operators, including the Riemann-Liouville, Holmgren, and Grünwald-Letnikov approaches given by different mathematicians like the Mellin transform which have established connections, while a few of them explored the relationships of the Hankel transform. In this survey, ideas from Kiryakov. V was taken especially related to a more unusual instance of kernels that were special functions like the Gauss and generalized hypergeometric functions, including arbitrary G-and H-functions, kernels and to create a theory of the associated GFC with several applications. Additionally, five more authors brought attention to their respective contributions in this area. In this survey, the Riemann-Liouville fractional integral is simplified to the Weyl integral, and a brief study is done on the hypergeometric functions of one and more variables, such as the generalized hypergeometric function contributed by a few mathematicians.
2024, Journal of Applied Analysis
In this paper, we study the stabilization problem of uncertain systems. We treat a class of uncertain systems whose nominal part is affine in the control and whose uncertain part is bounded by a known affine function of the control, when... more
In this paper, we study the stabilization problem of uncertain systems. We treat a class of uncertain systems whose nominal part is affine in the control and whose uncertain part is bounded by a known affine function of the control, when the control is bounded by a specified constant.
2024, Journal of Applied Analysis
In this paper, we study the stabilization problem of uncertain systems. We treat a class of uncertain systems whose nominal part is affine in the control and whose uncertain part is bounded by a known affine function of the control, when... more
In this paper, we study the stabilization problem of uncertain systems. We treat a class of uncertain systems whose nominal part is affine in the control and whose uncertain part is bounded by a known affine function of the control, when the control is bounded by a specified constant.
2024, HAL (Le Centre pour la Communication Scientifique Directe)
We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-dimensional Lie algebra (constructed in ) is a... more
We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-dimensional Lie algebra (constructed in ) is a generalization of the classical Virasoro algebra to the case of two space variables. Two main examples of integrable equations we obtain are quite well known. We show that the relation between these two equations is similar to that between the Korteweg-de Vries and Camassa-Holm equations.
2024, Journal of Applied Analysis
In this paper we investigate the existence and controllability of mild solutions to the first order semilinear evolution inclusions in Banach spaces with nonlocal conditions. We shall rely of a fixed point theorem for condensing maps due... more
In this paper we investigate the existence and controllability of mild solutions to the first order semilinear evolution inclusions in Banach spaces with nonlocal conditions. We shall rely of a fixed point theorem for condensing maps due to Martelli.
2024
For a fixed p and σ > −1, such that p > max{1, σ + 1}, one main concern of this paper is to find sufficient conditions for non solvability of ut = −(−∆) β 2 u − V (x)u + t σ h(x)u p + W (x, t), posed in ST := R N × (0, T), where 0 < T <... more
For a fixed p and σ > −1, such that p > max{1, σ + 1}, one main concern of this paper is to find sufficient conditions for non solvability of ut = −(−∆) β 2 u − V (x)u + t σ h(x)u p + W (x, t), posed in ST := R N × (0, T), where 0 < T < +∞, (−∆) β 2 with 0 < β ≤ 2 is the β/2 fractional power of the −∆, and W (x, t) = t γ w(x) ≥ 0. The potential V satisfies lim sup |x|→+∞ |V (x)||x| a < +∞, for some positive a. We shall see that the existence of solutions depends on the behavior at infinity of both initial data and the function h or of both w and h. The non-global existence is also discussed. We prove, among other things, that if u0(x) satisfies lim |x|→+∞ u p−1 0 (x)h(x)|x| (1+σ) inf{β,a} = +∞, any possible local solution blows up at a finite time for any locally integrable function W. The situation is then extended to nonlinear hyperbolic equations.
2024, Journal of Applied Analysis
The density topologies with respect to measure and category are motivation to consider the density topologies with respect to invariant σ-ideals on R. The properties of such topologies, including the separation axioms, are studied.
2024, Journal of Applied Analysis
We introduce a large class of contractive mappings, called Suzuki–Berinde type contraction. We show that any Suzuki–Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed... more
We introduce a large class of contractive mappings, called Suzuki–Berinde type contraction. We show that any Suzuki–Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mappings is also obtained. These results unify, generalize and complement various known comparable results in the literature.
2024, arXiv (Cornell University)
We introduce a large class of contractive mappings, called Suzuki Berinde type contraction. We show that any Suzuki Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed... more
We introduce a large class of contractive mappings, called Suzuki Berinde type contraction. We show that any Suzuki Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mapping is also obtained. These results unify, generalize and complement various known comparable results in the literature.
2024, Hacettepe Journal of Mathematics and Statistics
We study CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a semi-symmetric metric connection. Moreover, we obtain integrability conditions of the distributions on CR-submanifolds.
2024, Journal of Applied Analysis
Regular variation is an asymptotic property of functions and measures. The one variable theory is well-established, and has found numerous applications in both pure and applied mathematics. In this paper we present several new results on... more
Regular variation is an asymptotic property of functions and measures. The one variable theory is well-established, and has found numerous applications in both pure and applied mathematics. In this paper we present several new results on multivariable regular variation for functions and measures.
2024
In this paper we introduce and study an integral transform (Ỹ -transform) whose kernel is the Dμ,ρ(z) function which is generalized form of Kratzel function introduced by Kratzel [10]. First, we obtain the basic properties of Ỹ transform.... more
In this paper we introduce and study an integral transform (Ỹ -transform) whose kernel is the Dμ,ρ(z) function which is generalized form of Kratzel function introduced by Kratzel [10]. First, we obtain the basic properties of Ỹ transform. Further, we establish connection formulae of Ỹ -transform with Mellin transform, Laplace transform and Saigo operators. Next, we find the images of the product of H-function and SU V under this transform.
2024, Journal of Applied Analysis
The order structure of time projections associated with random times in a von Neumann algebra is investigated in the general setup as well as that of the CAR and CCR algebras. In the second case various additional properties (such as e.g.... more
The order structure of time projections associated with random times in a von Neumann algebra is investigated in the general setup as well as that of the CAR and CCR algebras. In the second case various additional properties (such as e.g. the upper/lower continuity) of the lattice of time projections are also discussed.
2024
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met,... more
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the possible limit distributions are precisely the operator-selfdecomposable laws.
2024, Journal of Applied Analysis
It is shown that the random transition count is complete for Markov chains with a fixed length and a fixed initial state, for some subsets of the set of all transition probabilities.
2024, International Organisations Research Journal
Twenty-five years have passed since the collapse of the Soviet Union (USSR) which led to the disruption of the regional check-and-balance system aimed at resolving national issues and political and socioeconomic contradictions. It also... more
Twenty-five years have passed since the collapse of the Soviet Union (USSR) which led to the disruption of the regional check-and-balance system aimed at resolving national issues and political and socioeconomic contradictions. It also resulted in a number of armed conflicts, including those in the Chechen Republic,
2024, Journal of Applied Analysis
In this paper we present some di erent types of ideal convergence/divergence and of ideal continuity for Riesz space-valued functions, and prove some basic properties and comparison results. We investigate the relations among di erent... more
In this paper we present some di erent types of ideal convergence/divergence and of ideal continuity for Riesz space-valued functions, and prove some basic properties and comparison results. We investigate the relations among di erent modes of ideal continuity and present a characterization of the ()-property for ideals of an abstract set. Finally we pose some open problems.
2024
We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of... more
We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is discribed by a first order differential equation and the material's behavior is modelled with a nonlinear elastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result of the weak solution. Moreover, we prove that the solution of the contact problem can be obtained as the limit of the solution of a regularized problem as the regularizaton parameter converges to 0. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.
2024, Journal of Applied Analysis
We study a system of quasilinear eigenvalue problems with Dirichlet boundary conditions on complete compact Riemannian manifolds. In particular, Cheng comparison estimates and the inequality of Faber–Krahn for the first eigenvalue of a (... more
We study a system of quasilinear eigenvalue problems with Dirichlet boundary conditions on complete compact Riemannian manifolds. In particular, Cheng comparison estimates and the inequality of Faber–Krahn for the first eigenvalue of a ( p , q ) {(p,q)} -Laplacian are recovered. Lastly, we reprove a Cheeger-type estimate for the p-Laplacian, 1 < p < ∞ {1
2024, Complex Variables and Elliptic Equations
Article (Accepted Version) http://sro.sussex.ac.uk Abolarinwa, Abimbola and Taheri, Ali (2021) Geometric estimates on weighted p-fundamental tone and applications to the first eigenvalue of submanifolds with bounded mean curvature.... more
Article (Accepted Version) http://sro.sussex.ac.uk Abolarinwa, Abimbola and Taheri, Ali (2021) Geometric estimates on weighted p-fundamental tone and applications to the first eigenvalue of submanifolds with bounded mean curvature. Complex Variables and Elliptic Equations: an international journal.
2024, Simon Stevin
We consider the problem utt + δut + εa∆u + ϕ(Ω |∇u| 2 dx)∆u ≥ f (x, t), posed in Ω × (0, +∞). Here Ω ⊂ R N is a an open smooth bounded domain and ϕ is like ϕ(s) = bs γ , γ > 0, a > 0 and ε = ±1. We prove, in certain conditions on f and ϕ... more
We consider the problem utt + δut + εa∆u + ϕ(Ω |∇u| 2 dx)∆u ≥ f (x, t), posed in Ω × (0, +∞). Here Ω ⊂ R N is a an open smooth bounded domain and ϕ is like ϕ(s) = bs γ , γ > 0, a > 0 and ε = ±1. We prove, in certain conditions on f and ϕ that there is absence of global solutions. The method of proof relies on a simple analysis of the ordinary inequality of the type w + δw ≥ αw + βw p. It is also shown that a global positive solution, when it exists, must decay at least exponentially.
2024
In this paper the nonexistence of global solutions to wave equations of the type u tt − ∆u ± u t = λ u + |u| 1+q is considered. We derive, for an averaging of solutions, a nonlinear second differential inequality of the type w ± w ≥ b w +... more
In this paper the nonexistence of global solutions to wave equations of the type u tt − ∆u ± u t = λ u + |u| 1+q is considered. We derive, for an averaging of solutions, a nonlinear second differential inequality of the type w ± w ≥ b w + |w| 1+q , and we prove a blowing up phenomenon under some restriction on u(x, 0) and u t (x, 0). Similar results are given for other equations.
2024
Various problems concerning probability measures on locally compact groups involve understanding what happens in the limit when a measure, or a sequence of measures, is operated upon by a sequence of automorphisms of the group. In the... more
Various problems concerning probability measures on locally compact groups involve understanding what happens in the limit when a measure, or a sequence of measures, is operated upon by a sequence of automorphisms of the group. In the case of Lie groups it turns out that much of the thrust of the questions can be reduced to studying the behaviour of measures on Euclidean spaces under linear transformations. Our aim here is to describe some simple properties in this respect and their applications to various problems; convergence of types, concentration functions, factor compactness, Levy's measures are some of the topics to which applications will be made.
2024, Journal of Computational and Applied Mathematics
We study boundary value problems of the form −∆u = f on Ω and Bu = g on the boundary ∂Ω, with either Dirichlet or Neumann boundary conditions, where Ω is a smooth bounded domain in R n and the data f, g are distributions. This problem has... more
We study boundary value problems of the form −∆u = f on Ω and Bu = g on the boundary ∂Ω, with either Dirichlet or Neumann boundary conditions, where Ω is a smooth bounded domain in R n and the data f, g are distributions. This problem has to be first properly reformulated and, for practical applications, it is of crucial importance is to obtain the continuity of the solution u in terms of f and g. For f = 0, taking advantage of the fact that u is harmonic on Ω, we provide four formulations of this boundary value problem (one using non-tangential limits of harmonic functions, one using Green functions, one using the Dirichlet-to-Neumann map, and a variational one); we show that these four formulations are equivalent. We provide a similar analysis for f = 0 and discuss the roles of f and g, which turn to be somewhat interchangeable in the low regularity case. The weak formulation is more convenient for numerical approximation, whereas the non-tangential limits definition is closer to the intuition and easier to check in concrete situations. We extend the weak formulation to polygonal domains using weighted Sobolev spaces. We also point out some new phenomena for the "concentrated loads" at the vertices in the polygonal case. Contents Introduction 1 1. The homogeneous Neumann problem 3 2. The inhomogeneous Neumann problem 11 3. Examples 12 4. Polygonal domains 13 5. The inhomogeneous Neumann problem revisited 15 References 17
2024, Zeitschrift für Analysis und ihre Anwendungen
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the... more
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the waves propagate at the same speed: using a frequency domain approach combined with multiplier technique, we prove that the system is exponentially stable when the coupling region is a subset of the damping region and satisfies the geometric control condition GCC (see Definition 1 below). Following a result of Haraux ([10]), we establish the main indirect observability inequality. This results leads, by the HUM method, to prove that the total system is exactly controllable by means of locally distributed control. In the second case, when the waves propagate at different speed, we establish an exponential decay rate in the weak energy space under appropriate geometric conditions. Consequently, the system is exactly controllable using a result of [10].
2024, HAL (Le Centre pour la Communication Scientifique Directe)
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the... more
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the waves propagate at the same speed: using a frequency domain approach combined with multiplier technique, we prove that the system is exponentially stable when the coupling region is a subset of the damping region and satisfies the geometric control condition GCC (see Definition 1 below). Following a result of Haraux ([10]), we establish the main indirect observability inequality. This results leads, by the HUM method, to prove that the total system is exactly controllable by means of locally distributed control. In the second case, when the waves propagate at different speed, we establish an exponential decay rate in the weak energy space under appropriate geometric conditions. Consequently, the system is exactly controllable using a result of [10].
2024, Journal of Mathematical Analysis and Applications
In this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing... more
In this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing Henstock-Kurzweil integrable functions.