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Memory effect phenomena and Г-convergence

Published online by Cambridge University Press:  14 November 2011

Maria Luisa Mascarenhas
Maria Luisa Mascarenhas
Affiliation:
Centra de Matemática e Aplicaçōes Fundamentals, C.M.A.F./I.N.I.C., Av. Prof. Gama Pinto 2, 1699 Lisboa Codex, Portugal
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Synopsis

It is known that the parametric equation u'∊+ a∊u∊ = f, u∊ (0)= 0,with α ≦ a∊ ≦ β, for all ∊ > 0 and almost everywhere in a bounded domain Ω of ℝN, and f in L∞((0, T) × Ω), shows, at the limit, a memory effect. In this work the associated minimisation problem is considered and we describe how the memory effect appears in the Γ-limit, for the weak topology H1:(0, T; L2(Ω)) of the corresponding functional. The sequence a∊ has no dependence in time.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 2 , 1993 , pp. 311 - 322
Copyright
Copyright © Royal Society of Edinburgh 1993

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