Autor(es):
Santos, Lisa 
; Rodrigues, José Francisco
Data: 2012
Identificador Persistente: http://hdl.handle.net/1822/19984
Origem: RepositóriUM - Universidade do Minho
Detalhes do Documento
Quasivariational solutions for first order quasilinear equations with gradient ...
Descrição
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable <em> a priori</em> estimates. We obtain also the existence of stationary solutions, by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results.
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable <em> a priori</em> estimates. We obtain also the existence of stationary solutions, by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results.
Tipo de Documento
Artigo
Idioma Inglês
Idioma Inglês
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