TY - JOUR
T1 - On the existence and 'blow-up' of solutions to a two-dimensional nonlinear boundary-value problem arising in corrosion modelling
AU - Kavian, Otared
AU - Vogelius, Michael
N1 - Funding Information:
This research was partly supported by NSF grantDsMS-0072556 and INT-0003788.
PY - 2003
Y1 - 2003
N2 - Let Ω be a bounded C2, αa domain in ℝ2. We prove that the boundary-value problem Δv = 0 in Ω, ∂v/∂n = λsinh(v) on ∂Ω, has infinitely many (classical) solutions for any given λ > 0. These solutions are constructed by means of a variational principle. We also investigate the limiting behaviour as λ → 0+; indeed, we prove that each of our solutions, as λ → 0+, after passing to a subsequence, develops a finite number of singularities located on ∂Ω.
AB - Let Ω be a bounded C2, αa domain in ℝ2. We prove that the boundary-value problem Δv = 0 in Ω, ∂v/∂n = λsinh(v) on ∂Ω, has infinitely many (classical) solutions for any given λ > 0. These solutions are constructed by means of a variational principle. We also investigate the limiting behaviour as λ → 0+; indeed, we prove that each of our solutions, as λ → 0+, after passing to a subsequence, develops a finite number of singularities located on ∂Ω.
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U2 - 10.1017/s0308210500002316
DO - 10.1017/s0308210500002316
M3 - Article
AN - SCOPUS:0037229004
SN - 0308-2105
VL - 133
SP - 119
EP - 149
JO - Royal Society of Edinburgh - Proceedings A
JF - Royal Society of Edinburgh - Proceedings A
IS - 1
ER -