Existence and blow up of solutions to certain classes of two-dimensional nonlinear Neumann problems

Kai Medville, Michael S. Vogelius

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 Δ uλ = 0 in Ω, ∂ uλ / ∂ n = D uλ + λ f (uλ) on ∂Ω. We place particular emphasis on f (u) = sinh (u) = frac((eu - e- u), 2), in which case the nonlinear flux boundary condition is frequently associated with the names of Butler and Volmer.

Original languageEnglish (US)
Pages (from-to)499-538
Number of pages40
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume23
Issue number4
DOIs
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

Keywords

  • Blow up
  • Critical points
  • Nonlinear Neumann boundary conditions

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