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

2018/05/16 by Fernando Miranda, Miranda, Fernando, José Francisco Rodrigues +3 · 2 citations
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1805.06190

openalex publication_date 2018/05/16 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

This paper considers a general framework for the study of the existence of\nquasi-variational and variational solutions to a class of nonlinear evolution\nsystems in convex sets of Banach spaces describing constraints on a linear\ncombination of partial derivatives of the solutions. The quasi-linear operators\nare of monotone type, but are not required to be coercive for the existence of\nweak solutions, which is obtained by a double penalisation/regularisation for\nthe approximation of the solutions. In the case of time-dependent convex sets\nthat are independent of the solution, we show also the uniqueness and the\ncontinuous dependence of the strong solutions of the variational inequalities,\nextending previous results to a more general framework.\n

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• An evolutionary vector-valued variational inequality and Lagrange multiplier

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