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TitleEvolutionary quasi-variational and variational inequalities with constraints on the derivatives
Author(s)Miranda, Fernando
Rodrigues, Jose Francisco
Santos, Lisa
Keywordsconstraints on the derivatives
Evolutionary quasi-variational inequalities
gradient constraints
Issue date2020
PublisherDe Gruyter
JournalAdvances in Nonlinear Analysis
Abstract(s)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 version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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