Topological Methods in Nonlinear Analysis

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

Jerzy A. Gawinecki and Wojciech M. Zajączkowski

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 39, Number 2 (2012), 263-284.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461243181

Mathematical Reviews number (MathSciNet)
MR2985881

Zentralblatt MATH identifier
1267.35228

Citation

Gawinecki, Jerzy A.; Zajączkowski, Wojciech M. Global existence of solutions to the nonlinear thermoviscoelasticity system with small data. Topol. Methods Nonlinear Anal. 39 (2012), no. 2, 263--284. https://projecteuclid.org/euclid.tmna/1461243181


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