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Global existence of weak-type solutions for models of monotone type in the theory of inelastic deformations

✍ Scribed by Krzysztof Chełmiński

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
271 KB
Volume
25
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

This article introduces the notion of weak‐type solutions for systems of equations from the theory of inelastic deformations, assuming that the considered model is of monotone type (for the definition see [Lecture Notes in Mathematics, 1998, vol. 1682]). For the boundary data associated with the initial‐boundary value problem and satisfying the safe‐load condition the existence of global in time weak‐type solutions is proved assuming that the monotone model is rate‐independent or of gradient type. Moreover, for models possessing an additional regularity property (see Section 5) the existence of global solutions in the sense of measures, defined by Temam in Archives for Rational Mechanics and Analysis, 95: 137, is obtained, too. Copyright © 2002 John Wiley & Sons, Ltd.

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