Analytic study of some Timoshenko systems

Abstract

In this dissertation, we are concerned with a nonlinear Timoshenko system modeling clamped thin elastic beams with time delay and a memory-type Timoshenko system with Dirichlet boundary conditions and a very general class of relaxation functions. For the nonlinear Timoshenko system with delay, under suitable assumptions on the data, we establish the well-posedness of the problem with respect to weak solutions and establish the exponential stability of the system under the usual equal wave speeds assumption, and we state the well-posedness of the system and establish its general stability considering the case of equal-speeds and the case of non-equal-speeds of propagation for the memory-type Timoshenko system.