On the existence and ‘blow-up’ of solutions to a two-dimensional nonlinear boundary-value problem arising in corrosion modelling
2003 ◽
Vol 133
(1)
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pp. 119-149
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Keyword(s):
Blow Up
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Let Ω be a bounded C2,α domain in R2. We prove that the boundary-value problem Δυ = 0 in Ω, ∂υ/∂n = λsinh(υ) 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.
2004 ◽
Vol 77
(4)
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pp. 700-706
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1987 ◽
Vol 26
(1-3)
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pp. 37-66
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2006 ◽
Vol 182
(2)
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pp. 181-221
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Keyword(s):
1983 ◽
Vol 52
(1)
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pp. 124-131
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2016 ◽
Vol 8
(1)
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pp. 49-55
Keyword(s):
2020 ◽
Vol 98
(2)
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pp. 100-109
Keyword(s):
Keyword(s):
2018 ◽
Vol 70
(3)
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pp. 410-421
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