Asymptotic behavior for a semilinear Bresse system with variable coefficients and locally distributed nonlinear dissipation

Abstract

In this paper, we consider a semilinear Bresse system in one dimensional bounded non homogeneous medium. We investigate stability issues for such a problem with a nonlinear damping acting in all three wave equations. We prove, firstly, the existence and uniqueness of the solutions by using the nonlinear semigroup method. Afterwords, we establish an uniform decay rates of the energy for these solutions without considering any restriction on the coefficients as well as the equality of the wave propagation speeds. Some techniques of the microlocal analysis theory are used in order to reach the desired asymptotics.