Evolutionary quasi-variational and variational inequalities with constraints on the derivatives

Author:

Miranda Fernando1ORCID,Rodrigues José Francisco2ORCID,Santos Lisa1ORCID

Affiliation:

1. CMAT – Departamento de Matemática , Escola de Ciências , Universidade do Minho , Campus de Gualtar, 4710-057 Braga , Portugal

2. CMAFcIO – Departamento de Matemática , Faculdade de Ciências , Universidade de Lisboa , P-1749-016 Lisboa , Portugal

Abstract

Abstract This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasi-linear operators are of monotone type, but are not required to be coercive for the existence of weak solutions, which is obtained by a double penalization/regularization for the approximation of the solutions. In the case of time-dependent convex sets that are independent of the solution, we show also the uniqueness and the continuous dependence of the strong solutions of the variational inequalities, extending previous results to a more general framework.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

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