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Title: Global existence result for thermoviscoelastic problems with hysteresis : dedicated to the memory of M. Schatzman
Authors: Paoli, LaetitiaPetrov, AdrienSchatzman, M.
Issue Date: 2011
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1616, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We consider viscoelastic solids undergoing thermal expansion and exhibiting hysteresis effects due to plasticity or phase transformations. Within the framework of generalized standard solids, the problem is described in a 3D setting by the momentum equilibrium equation, the flow rule describing the dependence of the stress on the strain history, and the heat transfer equation. Under appropriate regularity assumptions on the data, a local existence result for this thermodynamically consistent system is established, by combining existence results for ordinary differential equations in Banach spaces with a fixed-point argument. Then global estimates are obtained by using both the classical energy estimate and more specific techniques for the heat equation introduced by Boccardo and Gallouet. Finally a global existence result is derived.
Keywords: Existence result; generalized standard materials; heat equation; enthalpy transformation; maximal monotone operators; doubly nonlinear equations; plasticity; shape-memory alloys
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



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