### 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.

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.

#### Keywords

Nonlinear thermoviscoelasticity; initial-boundary value problem; local existence; global existence; Besov spaces; small data

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