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Presented at the COMSOL Multiphysics User's Conference 2005 Boston Irregular geometry - non-constant coefficient Map the region to a rectangle: liquid steel liquid steel Cauchy data Find lining: the interface between iron and furnace – Femlab Conference 2005 – 3
Presented at the COMSOL Multiphysics User's Conference 2005 Boston The Cauchy Problem for Laplace’s equation Classical ill-posed problem (Hadamard, 1900-1930) u xx + u yy = 0, u(x,0) = 0, −∞ ≤ x ≤ ∞, ∂u ∂x (x, 0) = 1 sin(nx), −∞ ≤ x ≤ ∞. n Solution: u(x,y) = 1 sin(nx) sinh(ny). n2 Large n: arbitrarily small data, arbitrarily large solution. The solution does not depend continuously on the data! – Femlab Conference 2005 – 4
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Numerical Solution of Cauchy Problems for Elliptic ... - COMSOL.com

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