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Global existence of solutions for non-small data to non-linear spherically symmetric thermoviscoelasticity

✍ Scribed by J. Gawinecki

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 231 KB
Volume: 26
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.406

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✦ Synopsis

Abstract

We consider some initial–boundary value problems for non‐linear equations of thermoviscoelasticity in the three‐dimensional case. Since, we are interested to prove global existence we consider spherically symmetric problem. We examine the Neumann conditions for the temperature and either the Neumann or the Dirichlet boundary conditions for the elasticity equations. Using the energy method, we are able to obtain some energy estimates in appropriate Sobolev spaces enough to prove existence for all time without any restrictions on data. Due to the spherical symmetricity the constants in the above estimates increase with time so the existence for all finite times is proved only. Copyright © 2003 John Wiley & Sons, Ltd.

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