Existence and blow up of solutions to certain classes of two-dimensional nonlinear Neumann problems
Kai Medville
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USAMichael S. Vogelius
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA
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Abstract
In this paper we study, analytically and numerically, the existence and blow up of solutions to two-dimensional boundary value problems of the form in , on . We place particular emphasis on , in which case the nonlinear flux boundary condition is frequently associated with the names of Butler and Volmer.
Résumé
Dans cet article nous étudions, analytiquement et numériquement, l'existence et l'explosion de solutions de problèmes aux limites bi-dimensionnels de la forme dans , sur . Nous portons une attention particulière à , situation dans laquelle la condition non linéaire sur le flux au bord est fréquemment associée aux noms de Butler et Volmer.
Cite this article
Kai Medville, Michael S. Vogelius, Existence and blow up of solutions to certain classes of two-dimensional nonlinear Neumann problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 4, pp. 499–538
DOI 10.1016/J.ANIHPC.2005.02.008