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Papers by aissa guesmia

Annales Polonici Mathematici, 2005

ABSTRACT We consider an initial boundary value problem for the equation u tt -𝛥u-∇ϕ·∇u+f(u)+g(u t... more ABSTRACT We consider an initial boundary value problem for the equation u tt -𝛥u-∇ϕ·∇u+f(u)+g(u t )=0. We first prove local and global existence results under suitable conditions on f and g. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of g. This result improves and includes earlier decay results established by the authors.

Nodea-nonlinear Differential Equations and Applications

This work is concerned with a system of two viscoelastic wave equations with nonlinear damping an... more This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and Liu (Nonlinear Anal. 71:2257–2267, 2009) in which only the exponential and polynomial decay rates are considered.

Mathematical Methods in The Applied Sciences, 2009

In this paper we consider the following Timoshenko system: with Dirichlet boundary conditions and... more In this paper we consider the following Timoshenko system: with Dirichlet boundary conditions and initial data where a, b, g and h are specific functions and ρ1, ρ2, k1, k2 and L are given positive constants. We establish a general stability estimate using the multiplier method and some properties of convex functions. Without imposing any growth condition on h at the origin, we show that the energy of the system is bounded above by a quantity, depending on g and h, which tends to zero as time goes to infinity. Our estimate allows us to consider a large class of functions h with general growth at the origin. We use some examples (known in the case of wave equations and Maxwell system) to show how to derive from our general estimate the polynomial, exponential or logarithmic decay. The results of this paper improve and generalize some existing results in the literature and generate some interesting open problems. Copyright © 2009 John Wiley & Sons, Ltd.

Applied Mathematics and Computation, 2008

Annales Polonici Mathematici, 2005

ABSTRACT We consider an initial boundary value problem for the equation u tt -𝛥u-∇ϕ·∇u+f(u)+g(u t... more ABSTRACT We consider an initial boundary value problem for the equation u tt -𝛥u-∇ϕ·∇u+f(u)+g(u t )=0. We first prove local and global existence results under suitable conditions on f and g. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of g. This result improves and includes earlier decay results established by the authors.

Nodea-nonlinear Differential Equations and Applications

This work is concerned with a system of two viscoelastic wave equations with nonlinear damping an... more This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and Liu (Nonlinear Anal. 71:2257–2267, 2009) in which only the exponential and polynomial decay rates are considered.

Mathematical Methods in The Applied Sciences, 2009

In this paper we consider the following Timoshenko system: with Dirichlet boundary conditions and... more In this paper we consider the following Timoshenko system: with Dirichlet boundary conditions and initial data where a, b, g and h are specific functions and ρ1, ρ2, k1, k2 and L are given positive constants. We establish a general stability estimate using the multiplier method and some properties of convex functions. Without imposing any growth condition on h at the origin, we show that the energy of the system is bounded above by a quantity, depending on g and h, which tends to zero as time goes to infinity. Our estimate allows us to consider a large class of functions h with general growth at the origin. We use some examples (known in the case of wave equations and Maxwell system) to show how to derive from our general estimate the polynomial, exponential or logarithmic decay. The results of this paper improve and generalize some existing results in the literature and generate some interesting open problems. Copyright © 2009 John Wiley & Sons, Ltd.

Applied Mathematics and Computation, 2008

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