Global existence of solutions to the nonlinear thermoviscoelasticity system with small data

Abstract

We consider the nonlinear system of partial differential equations describing the thermoviscoelastic medium ocupied a bounded domain $\Omega\subset\mathbb{R}^3$. We proved the global existence (in time) of solution for the nonlinear thermoviscoelasticity system for the initial-boundary value problem with the Dirichlet boundary conditions for the displacement vector and the heat flux at the boundary. In the proof we assume some growth conditions on nonlinearity and some smallness conditions on data in some norms.