Global existence and stability for a coupled system of quasilinear viscoelastic equations

In this paper we investigate the global existence and stability of solutions to the initial-boundary-value problem for a coupled system of two quasi-linear viscoelastic equations with variable exponents. For general initial data and variables exponents, we establish a global existence theorem of solutions to the initial-boundary-value problem by virtue of some new functionals. Moreover, using the Sobolev embedding inequality, the Poincare inequality, and other in-equalities and estimation techniques, we obtain the uniform exponential decay rate for the solution energy of the coupled system of two quasilinear viscoelastic equations.