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Unique Global Solvability in Two-Dimensional Nonlinear Termoelasticity
Subtitle:Raport Badawczy = Research Report ; RB/12/2002
Creator:Pawłow, Irena ; Zajączkowski, Wojciech
Publisher:Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences
Place of publishing: Date issued/created: Description:45 stron ; 21 cm ; Bibliografia s. 45
Subject and Keywords:Global existence ; Globalna egzystencja ; Parabolic regularization ; Paraboliczna regularyzacja ; Non- linear thermoelasticity
Abstract:The paper is concerned with initial-boundary value problem in two-dimensional nonlinear thermoelasticity which arises as a mathematical model of shape memory materials. The problem has the form of viscoelasticity system with capillarity coupled with heat conducstion equation with mechanical dissipation. The corresponding elastic energy is a nonconvex multiple-weel function of strain, with the shape changing qualitatively with temperature. Under assumption on the growth of this energy with respect to temperature, the existence and uniqueness of a global-in-time solutions for large data has been proven. The existence proof is based on parabolic decomposition of the elastiity system and application of the Leray-Schauder fixed point theorem. The main part of the proof consists in deriving Holder a priori estimates by succesive improvement of energy estimates.
Relation:Raport Badawczy = Research Report
Resource type: Detailed Resource Type: Source: Language: Language of abstract: Rights:Licencja Creative Commons Uznanie autorstwa 4.0
Terms of use:Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -
Digitizing institution:Instytut Badań Systemowych Polskiej Akademii Nauk
Original in:Biblioteka Instytutu Badań Systemowych PAN
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