TY - JOUR
T1 - Existence and blow up of solutions to certain classes of two-dimensional nonlinear Neumann problems
AU - Medville, Kai
AU - Vogelius, Michael S.
N1 - Funding Information:
This research was partially supported by NSF grants DMS–0307119 and INT–0003788. Part of this work was carried out during a stay by the second author at Université Joseph Fourier, Grenoble. He wishes to thank Eric Bonnetier for making this visit a most rewarding one.
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
KW - Blow up
KW - Critical points
KW - Nonlinear Neumann boundary conditions
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U2 - 10.1016/j.anihpc.2005.02.008
DO - 10.1016/j.anihpc.2005.02.008
M3 - Article
AN - SCOPUS:33745713341
SN - 0294-1449
VL - 23
SP - 499
EP - 538
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 4
ER -