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

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

A classical three-dimensional 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 constitutes a priori e...

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Veröffentlicht in:SIAM journal on mathematical analysis 2013-01, Vol.45 (4), p.1997-2045
Hauptverfasser: Pawlow, Irena, Zajaczkowski, Wojciech M
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Approximation
Boundary conditions
Conventions
Cybernetics
Estimates
Heat conductivity
Intervals
Mathematical analysis
Norms
Phase transitions
Sobolev space
Three dimensional
Uniqueness
Viscosity
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Zusammenfassung:A classical three-dimensional 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 constitutes 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. [PUBLICATION ABSTRACT]
ISSN:0036-1410
1095-7154
DOI:10.1137/110859026