Mohammad Kafini

A blow-up result in a Cauchy viscoelastic problem

In this work we consider a Cauchy problem for a nonlinear viscoelastic equation. Under suitable conditions on the initial data and the relaxation function, we prove a finite-time blow-up result.

On the uniform decay in viscoelastic problems in Rn

In this paper we consider a linear Cauchy viscoelastic problem. We show that, for compactly supported initial data and for an exponentially decaying relaxation function, the decay of the first energy of solution is polynomial. The finite-speed propagation is used to compensate for the lack of Poincares inequality in R^n.

Energy decay result in a Timoshenko-type system of thermoelasticity of type III with distributive delay

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with distributive delay, where the heat conduction is given by Green and Naghdi theories. We establish the stability of the system for the case of equal and nonequal speeds of wave propagation.

A decay result to a viscoelastic problem in Rn with an oscillating kernel

In this paper we consider a linear Cauchy viscoelastic problem. We show that, for compactly supported initial data and for not necessarily decreasing (oscillating) relaxation function, the decay of the first energy of solutions is polynomial. The proof relies on some appropriately chosen functionals. The combination of which satisfies a certain integral inequality.

On the stabilization of a Cauchy viscoelastic problem with singular kernel and nonlinear source term

A viscoelastic Cauchy problem subjected to a nonlinear source term is investigated. The memory term in the system involves a kernel which is not regular as is usually the case. It is proved that solutions go to zero in a polynomial manner as time goes to infinity.

Local existence and blow up of solutions to a logarithmic nonlinear wave equation with delay

ABSTRACT This paper is concerned with a problem of a logarithmic nonlinear wave equation with delay. The local existence result has been established using the semigroup theory. In addition, for negative initial energy, a finite-time blow-up result is proved.