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Lq-almost solvability of inelastic models of monotone type

Published online by Cambridge University Press:  15 July 2011

Sergiy Nesenenko
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany (nesenenko@mathematik.tu-darmstadt.de) and Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252 Paris Cedex 05, France

Abstract

It is well known that the loss of the coerciveness for governing monotone nonlinearities in evolution equations/inclusions can lead to the problem having no solution for given data, and the rule for choosing appropriate data has to be prescribed. Allowing constitutive functions in the evolution relations for elasto-/visco-plastic models of monotone type to be non-coercive, we first give a new (relaxed) meaning to the solvability of the systems of equations under consideration and then we define criteria for choosing admissible data, which guarantees the solvability in the defined sense. Realizing this strategy, a slight extension of the well-developed monotone-operator method to our needs is performed. The theory is applied to some well-known models in elasto-/visco-plasticity. The relations between the standard notion of the solvability and defined one are investigated.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2011

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