Wladimir Neves - Academia.edu (original) (raw)

Papers by Wladimir Neves

arXiv (Cornell University), Apr 15, 2024

This paper proposes a new approach to solving the Buckley-Leverett System, which is to consider a... more This paper proposes a new approach to solving the Buckley-Leverett System, which is to consider a compressible approximation model characterized by a stiff pressure law. Passing to the incompressible limit, the compressible model gives rise to a Hele-Shaw type free boundary limit of Buckley-Leverett System, and it is shown the existence of a weak solution of it.

In this paper some important inequalities are revisited. First, as motivation, we give another pr... more In this paper some important inequalities are revisited. First, as motivation, we give another proof of the Hardy's inequality applying convenient vector fields as introduced by Mitidieri, see [6]. Then, we investigate a particular case of the Caffarelli-Kohn-Nirenberg's inequality. Finally, we study the Rellic's inequality.

Nonlinear Analysis-real World Applications, Dec 1, 2023

We study a new nonlocal approach to the mathematical modelling of the Chemotaxis problem, which d... more We study a new nonlocal approach to the mathematical modelling of the Chemotaxis problem, which describes the random motion of a certain population due a substance concentration. Considering the initialboundary value problem for the fractional hyperbolic Keller-Segel model, we prove the solvability of the problem. The solvability result relies mostly on fractional calculus and kinetic formulation of scalar conservation laws.

arXiv (Cornell University), Mar 28, 2013

We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension... more We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted Sobolev space with low regularity in the weight. The method used can be applied for other nonlinear dispersive models, for instance the multidimensional nonlinear Schrödinger equation.

arXiv (Cornell University), Jul 8, 2010

In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm ... more In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN operators contains the algebra of the compact ones.

Communications in Mathematical Sciences, 2022

We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate pa... more We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we impose a Dirichlet boundary condition and in the another one a Neumann condition. Under this mixed-boundary condition, we show the existence of solutions for measurable and bounded non-negative initial data. The nonlocal anisotropic diffusion effect relies on an inverse of a s−fractional type elliptic operator, and the solvability is proved for any s ∈ (0, 1).

arXiv (Cornell University), Oct 6, 2022

We are concerned in this paper with the degenerate fractional diffusion advection equations posed... more We are concerned in this paper with the degenerate fractional diffusion advection equations posed in bounded domains. Due to a suitable formulation, we show the existence of weak entropy solutions for measurable and bounded initial and Dirichlet boundary data. Moreover, we prove a L 1 −type contraction property for weak entropy solutions obtained via parabolic perturbation. This is a weak selection principle which means that the weak entropy solutions are stable in this class.

arXiv (Cornell University), Jul 24, 2013

We consider the stochastic divergence-free continuity equations with Ladyzhenskaya-Prodi-Serrin c... more We consider the stochastic divergence-free continuity equations with Ladyzhenskaya-Prodi-Serrin condition. Wellposedness is proved meanwhile uniqueness may fail for the deterministic PDE. The main issue of strong uniqueness, in the probabilistic sense, relies on stochastic characteristic method and the generalized Itô-Wentzell-Kunita formula. The stability property for the unique solution is proved with respect to the initial data. Moreover, a persistence result is established by a representation formula.

The articles of this volume will be reviewed individually. For Part I see Zbl 1215.35007.

Mathematical Models and Methods in Applied Sciences, May 21, 2018

In this talk, we consider a fractional type degenerate heat equation posed in bounded domains. We... more In this talk, we consider a fractional type degenerate heat equation posed in bounded domains. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition. The nonlocal diffusion effect relies on an inverse of the sfractional Laplacian operator, and the solvability is proved for any s , 0 < s < 1.

Journal of Differential Equations, Oct 1, 2011

In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient u p W 1,p (Ω... more In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient u p W 1,p (Ω) / u p L q (∂Ω) among functions that vanish in a set contained on the boundary ∂Ω of given boundary measure. We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set.

Journal of Differential Equations, Aug 1, 2003

We study the initial-boundary-value problems for multidimensional scalar conservation laws in non... more We study the initial-boundary-value problems for multidimensional scalar conservation laws in noncylindrical domains with Lipschitz boundary. We show the existenceuniqueness of this problem for initial-boundary data in L ∞ and the flux-function in the class C 1. In fact, first considering smooth boundary, we obtain the L 1contraction property, discuss the existence problem and prove it by the Young measures theory. In the end we show how to pass the existence-uniqueness results on to some domains with Lipschitz boundary.

arXiv (Cornell University), Dec 4, 2021

We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate pa... more We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we impose a Dirichlet boundary condition and in the another one a Neumann condition. Under this mixed-boundary condition, we show the existence of solutions for measurable and bounded non-negative initial data. The nonlocal anisotropic diffusion effect relies on an inverse of a s−fractional type elliptic operator, and the solvability is proved for any s ∈ (0, 1).

arXiv (Cornell University), Apr 9, 2013

In this paper we study the theory of operators on complex Hilbert spaces, which attain their mini... more In this paper we study the theory of operators on complex Hilbert spaces, which attain their minimum in the unit sphere. We prove some important results concerning the characterization of the N*, and also AN* operators, see respectively Definition 1.1 and Definition 1.3. The injective property plays an important role in these operators, and shall be established by these classes.

arXiv (Cornell University), Nov 17, 2016

We are concerned with the theory of existence and uniqueness of flows generated by divergence fre... more We are concerned with the theory of existence and uniqueness of flows generated by divergence free vector fields with compact support. Hence, assuming that the velocity vector fields are measurable, bounded, and the flows in the Euclidean space are measure preserving, we show two counterexamples of uniqueness/existence for such flows. First we consider the autonomous case in dimension 3, and then, the non autonomous one in dimension 2.

Springer proceedings in mathematics & statistics, Aug 28, 2013

We propose a new approach to the mathematical modeling of the Buckley-Leverett system, which desc... more We propose a new approach to the mathematical modeling of the Buckley-Leverett system, which describes two-phase flows in porous media. Considering the initial-boundary value problem for a deduced model, we prove the solvability of the problem. The solvability result relies mostly on the kinetic method.

arXiv (Cornell University), Mar 18, 2010

Applying an Abstract Interpolation Lemma, we can show persistence of solutions of the initial val... more Applying an Abstract Interpolation Lemma, we can show persistence of solutions of the initial value problem to higher order nonlinear Schrödinger equation, also called Airy-Schrödinger equation, in weighted Sobolev spaces X 2,θ , for 0 ≤ θ ≤ 1.

arXiv (Cornell University), May 27, 2013

Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning multi-time Hamilton-Jacobi e... more Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning multi-time Hamilton-Jacobi equations, we introduce the theory of multitime systems of conservation laws. We show the existence and uniqueness of solution to the Cauchy problem for a system of multi-time conservation laws with two independent time variables in one space dimension. Our proof relies on a suitable generalization of the Lax-Oleinik formula.

arXiv (Cornell University), Apr 5, 2013

We consider the general Caffarelli-Kohn-Nirenberg inequality in the Euclidean and Remannian setti... more We consider the general Caffarelli-Kohn-Nirenberg inequality in the Euclidean and Remannian setting. From a new parameter introduced, the proof of the former case, follows by simple interpolation arguments and Hölder's inequality. Moreover, the ranges of this convenient parameter completely characterize the inequality. Secondly, the same technics are used to study the Caffarelli-Kohn-Nirenberg inequality in the Riemannian case.

arXiv (Cornell University), Jul 29, 2008

Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Ri... more Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L 1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L 1 norm is of order h 1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theory which was originally developed in the Euclidian setting. We extent the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.

arXiv (Cornell University), Apr 15, 2024

This paper proposes a new approach to solving the Buckley-Leverett System, which is to consider a... more This paper proposes a new approach to solving the Buckley-Leverett System, which is to consider a compressible approximation model characterized by a stiff pressure law. Passing to the incompressible limit, the compressible model gives rise to a Hele-Shaw type free boundary limit of Buckley-Leverett System, and it is shown the existence of a weak solution of it.

In this paper some important inequalities are revisited. First, as motivation, we give another pr... more In this paper some important inequalities are revisited. First, as motivation, we give another proof of the Hardy's inequality applying convenient vector fields as introduced by Mitidieri, see [6]. Then, we investigate a particular case of the Caffarelli-Kohn-Nirenberg's inequality. Finally, we study the Rellic's inequality.

Nonlinear Analysis-real World Applications, Dec 1, 2023

We study a new nonlocal approach to the mathematical modelling of the Chemotaxis problem, which d... more We study a new nonlocal approach to the mathematical modelling of the Chemotaxis problem, which describes the random motion of a certain population due a substance concentration. Considering the initialboundary value problem for the fractional hyperbolic Keller-Segel model, we prove the solvability of the problem. The solvability result relies mostly on fractional calculus and kinetic formulation of scalar conservation laws.

arXiv (Cornell University), Mar 28, 2013

We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension... more We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted Sobolev space with low regularity in the weight. The method used can be applied for other nonlinear dispersive models, for instance the multidimensional nonlinear Schrödinger equation.

arXiv (Cornell University), Jul 8, 2010

In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm ... more In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN operators contains the algebra of the compact ones.

Communications in Mathematical Sciences, 2022

We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate pa... more We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we impose a Dirichlet boundary condition and in the another one a Neumann condition. Under this mixed-boundary condition, we show the existence of solutions for measurable and bounded non-negative initial data. The nonlocal anisotropic diffusion effect relies on an inverse of a s−fractional type elliptic operator, and the solvability is proved for any s ∈ (0, 1).

arXiv (Cornell University), Oct 6, 2022

We are concerned in this paper with the degenerate fractional diffusion advection equations posed... more We are concerned in this paper with the degenerate fractional diffusion advection equations posed in bounded domains. Due to a suitable formulation, we show the existence of weak entropy solutions for measurable and bounded initial and Dirichlet boundary data. Moreover, we prove a L 1 −type contraction property for weak entropy solutions obtained via parabolic perturbation. This is a weak selection principle which means that the weak entropy solutions are stable in this class.

arXiv (Cornell University), Jul 24, 2013

We consider the stochastic divergence-free continuity equations with Ladyzhenskaya-Prodi-Serrin c... more We consider the stochastic divergence-free continuity equations with Ladyzhenskaya-Prodi-Serrin condition. Wellposedness is proved meanwhile uniqueness may fail for the deterministic PDE. The main issue of strong uniqueness, in the probabilistic sense, relies on stochastic characteristic method and the generalized Itô-Wentzell-Kunita formula. The stability property for the unique solution is proved with respect to the initial data. Moreover, a persistence result is established by a representation formula.

The articles of this volume will be reviewed individually. For Part I see Zbl 1215.35007.

Mathematical Models and Methods in Applied Sciences, May 21, 2018

In this talk, we consider a fractional type degenerate heat equation posed in bounded domains. We... more In this talk, we consider a fractional type degenerate heat equation posed in bounded domains. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition. The nonlocal diffusion effect relies on an inverse of the sfractional Laplacian operator, and the solvability is proved for any s , 0 < s < 1.

Journal of Differential Equations, Oct 1, 2011

In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient u p W 1,p (Ω... more In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient u p W 1,p (Ω) / u p L q (∂Ω) among functions that vanish in a set contained on the boundary ∂Ω of given boundary measure. We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set.

Journal of Differential Equations, Aug 1, 2003

We study the initial-boundary-value problems for multidimensional scalar conservation laws in non... more We study the initial-boundary-value problems for multidimensional scalar conservation laws in noncylindrical domains with Lipschitz boundary. We show the existenceuniqueness of this problem for initial-boundary data in L ∞ and the flux-function in the class C 1. In fact, first considering smooth boundary, we obtain the L 1contraction property, discuss the existence problem and prove it by the Young measures theory. In the end we show how to pass the existence-uniqueness results on to some domains with Lipschitz boundary.

arXiv (Cornell University), Dec 4, 2021

We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate pa... more We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we impose a Dirichlet boundary condition and in the another one a Neumann condition. Under this mixed-boundary condition, we show the existence of solutions for measurable and bounded non-negative initial data. The nonlocal anisotropic diffusion effect relies on an inverse of a s−fractional type elliptic operator, and the solvability is proved for any s ∈ (0, 1).

arXiv (Cornell University), Apr 9, 2013

In this paper we study the theory of operators on complex Hilbert spaces, which attain their mini... more In this paper we study the theory of operators on complex Hilbert spaces, which attain their minimum in the unit sphere. We prove some important results concerning the characterization of the N*, and also AN* operators, see respectively Definition 1.1 and Definition 1.3. The injective property plays an important role in these operators, and shall be established by these classes.

arXiv (Cornell University), Nov 17, 2016

We are concerned with the theory of existence and uniqueness of flows generated by divergence fre... more We are concerned with the theory of existence and uniqueness of flows generated by divergence free vector fields with compact support. Hence, assuming that the velocity vector fields are measurable, bounded, and the flows in the Euclidean space are measure preserving, we show two counterexamples of uniqueness/existence for such flows. First we consider the autonomous case in dimension 3, and then, the non autonomous one in dimension 2.

Springer proceedings in mathematics & statistics, Aug 28, 2013

We propose a new approach to the mathematical modeling of the Buckley-Leverett system, which desc... more We propose a new approach to the mathematical modeling of the Buckley-Leverett system, which describes two-phase flows in porous media. Considering the initial-boundary value problem for a deduced model, we prove the solvability of the problem. The solvability result relies mostly on the kinetic method.

arXiv (Cornell University), Mar 18, 2010

Applying an Abstract Interpolation Lemma, we can show persistence of solutions of the initial val... more Applying an Abstract Interpolation Lemma, we can show persistence of solutions of the initial value problem to higher order nonlinear Schrödinger equation, also called Airy-Schrödinger equation, in weighted Sobolev spaces X 2,θ , for 0 ≤ θ ≤ 1.

arXiv (Cornell University), May 27, 2013

Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning multi-time Hamilton-Jacobi e... more Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning multi-time Hamilton-Jacobi equations, we introduce the theory of multitime systems of conservation laws. We show the existence and uniqueness of solution to the Cauchy problem for a system of multi-time conservation laws with two independent time variables in one space dimension. Our proof relies on a suitable generalization of the Lax-Oleinik formula.

arXiv (Cornell University), Apr 5, 2013

We consider the general Caffarelli-Kohn-Nirenberg inequality in the Euclidean and Remannian setti... more We consider the general Caffarelli-Kohn-Nirenberg inequality in the Euclidean and Remannian setting. From a new parameter introduced, the proof of the former case, follows by simple interpolation arguments and Hölder's inequality. Moreover, the ranges of this convenient parameter completely characterize the inequality. Secondly, the same technics are used to study the Caffarelli-Kohn-Nirenberg inequality in the Riemannian case.

arXiv (Cornell University), Jul 29, 2008

Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Ri... more Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L 1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L 1 norm is of order h 1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theory which was originally developed in the Euclidian setting. We extent the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.