Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/2898

TitleA parabolic quasi-variational inequality arising in a superconductivity model
Author(s)Rodrigues, José Francisco
Santos, Lisa
Issue date2000
PublisherScuola Normale Superiore di Pisa
Citation"Annali della Scuola Normale Superiore di Pisa. Classe di Scienze". ISSN 0391-173X. 29 (2000) 153-169.
Abstract(s)We consider the existence of solutions for a parabolic quasilinear problem with a gradient constraint which threshold depends on the solution itself. The problem may be considered as a quasi-variational inequality and the existence of solution is shown by considering a suitable family of approximating quasilinear equations of p-Laplacian type. A priori estimates on the time derivative of the approximating solutions and on the nonlinear diffusion coefficients are used in the passage to the limit, as well as a suitable sequence of convex sets with variable gradient constraint. The asymptotic behaviour as t → ∞ is also considered, and the solutions of the quasi-variational inequality are shown to converge, at least for subsequences, to a solution of a stationary quasi-variational inequality. These results can be applied to the critical-state model of type-II superconductors in longitudinal geometry.
TypeArticle
Description35K85 (primary), 35K55, 35R35 (secondary)
URIhttp://hdl.handle.net/1822/2898
ISSN0391-173X
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals
DMAT - Artigos (Papers)

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