Memory effect phenomena and Г-convergence
Maria Luisa Mascarenhas · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1993
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 ℝ N , 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 H 1 :(0, T; L 2 (Ω)) of the corresponding functional. The sequence a ∊ has no dependence in time.