On regular solutions to two-dimensional thermoviscoelasticity

Volume 43 / 2016

Jerzy A. Gawinecki, Wojciech M. Zajączkowski Applicationes Mathematicae 43 (2016), 207-233 MSC: Primary 74B20, 35K50; Secondary 35Q72, 74F05. DOI: 10.4064/am2299-6-2016 Published online: 23 September 2016

Abstract

A two-dimensional thermoviscoelastic system of Kelvin–Voigt type with strong dependence on temperature is considered. The existence and uniqueness of a global regular solution is proved without small data assumptions. The global existence is proved in two steps. First, a global a priori estimate is derived by applying anisotropic Sobolev spaces with a mixed norm. Then local existence, proved by the method of successive approximations for a sufficiently small time interval, is extended step by step in time. By a two-dimensional solution we mean that all the relevant quantities depend on two space variables only.

Authors

  • Jerzy A. GawineckiInstitute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    S. Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail
  • Wojciech M. ZajączkowskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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