Geodesic
On regular solutions to two-dimensional thermoviscoelasticity
Jerzy A. Gawinecki 1   ; Wojciech M. Zajączkowski 2
1 Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology S. Kaliskiego 2 00-908 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland
Applicationes Mathematicae, Tome 43 (2016) no. 2, pp. 207-233 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am2299-6-2016
Keywords: two dimensional thermoviscoelastic system kelvin voigt type strong dependence temperature considered existence uniqueness nbsp global regular solution proved without small assumptions global existence proved steps first global priori estimate derived applying anisotropic sobolev spaces nbsp mixed norm local existence proved method successive approximations nbsp sufficiently small time interval extended step step time two dimensional solution mean relevant quantities depend space variables only

Jerzy A. Gawinecki  1   ; Wojciech M. Zajączkowski  2

1 Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology S. Kaliskiego 2 00-908 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland 
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Jerzy A. Gawinecki; Wojciech M. Zajączkowski. On regular solutions to two-dimensional thermoviscoelasticity. Applicationes Mathematicae, Tome 43 (2016) no. 2, pp. 207-233. doi: 10.4064/am2299-6-2016

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