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On wave equation: review and recent results

The aim of this paper is to give an overview of results related to nonlinear wave equations during the last half century. In this regard, we present results concerning existence, decay and blow up for classical nonlinear equations. After that, we discuss briefly some important results of the variable-exponent Lebesgue and Sobolev spaces. Results related to nonexistence and blow...

Energy decay in a Timoshenko-type system of thermoelasticity of type III with different wave-propagation speeds

In this paper, we consider a one-dimensional linear Timoshenko system of thermoelasticity type III and prove a polynomial stability result for the non-equal wave-propagation speed case.

General decay of solutions of a nonlinear system of viscoelastic wave equations

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...

On the Internal and Boundary Stabilization of Timoshenko Beams

Salim A. Messaoudi 0 Muhammad I. Mustafa 0 0 Muhammad I. Mustafa King Fahd University of Petroleum and Minerals Department of Mathematics and Statistics Dhahran 31261 Saudi Arabia In this paper we