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

• Autor(a) principal: Miranda, Fernando
• Data de Publicação: 2020
• Outros Autores: Rodrigues, Jose Francisco, Santos, Lisa
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/65606
• topic: constraints on the derivatives; Evolutionary quasi-variational inequalities; gradient constraints; Ciências Naturais::Matemáticas; Science & Technology

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.