Global Regular Solutions to a Kelvin-Voigt Type Thermoviscoelastic System

Details Global Regular Solutions to a Kelvin-Voigt Type Thermoviscoelastic System Global Regular Solutions to a Kelvin-Voigt Type Thermoviscoelastic System

2011-12-14

arxiv.org/abs/1112.3176v1

Mathematics

Analysis of PDEs

52 pages

Scientific paper

A classical 3-D thermoviscoelastic system of Kelvin-Voigt type is considered. The existence and uniqueness of a global regular solution is proved without small data assumption. The existence proof is based on the successive approximation method. The crucial part constitute a priori estimates on an arbitrary finite time interval, which are derived with the help of the theory of anisotropic Sobolev spaces with a mixed norm.

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