Singular limits of a two-dimensional boundary value problem arising in corrosion modelling
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Date
2006
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Abstract
We consider the boundary value problem
Du = 0 in Omega, partial derivative u/partial derivative v = 2 lambda sinh u on partial derivative Omega
where Omega is a smooth and bounded domain in R(2) and lambda > 0. We prove that for any integer k >= 1 there exist at least two solutions u (lambda) with the property that the boundary flux satisfies up to subsequences lambda -> 0,
2 lambda sinh(mu(lambda)) -> 2 pi Sigma(2k)(j=1)(-1)(j-1 delta)xi(,)(j)
where the xi (j) are points of partial derivative Omega ordered clockwise in j.
Du = 0 in Omega, partial derivative u/partial derivative v = 2 lambda sinh u on partial derivative Omega
where Omega is a smooth and bounded domain in R(2) and lambda > 0. We prove that for any integer k >= 1 there exist at least two solutions u (lambda) with the property that the boundary flux satisfies up to subsequences lambda -> 0,
2 lambda sinh(mu(lambda)) -> 2 pi Sigma(2k)(j=1)(-1)(j-1 delta)xi(,)(j)
where the xi (j) are points of partial derivative Omega ordered clockwise in j.