doi:10.4208/eajam.100913.061113a

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Publication Date

Fri Nov 01 2013

Journal Name

East Asian Journal On Applied Mathematics

Volume

3

DOI

10.4208/eajam.100913.061113a

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Free Boundary Determination in Nonlinear Diffusion

M. S.

D.

M.

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Abstract<p>Free boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the <italic>lsqnonlin</italic> routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, instability is manifest in the derivative of the moving free surface, but not in the free surface itself nor in the concentration or temperature.</p>

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