Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/19984

TitleQuasivariational solutions for first order quasilinear equations with gradient constraint
Author(s)Santos, Lisa
Rodrigues, José Francisco
Issue date2012
PublisherSpringer
JournalArchive for Rational Mechanics and Analysis
Abstract(s)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.
TypeArticle
URIhttp://hdl.handle.net/1822/19984
DOI10.1007/s00205-012-0511-x
ISSN0003-9527
Publisher versionhttp://dx.doi.org/10.1007/s00205-012-0511-x
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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