Surface integrals approach to solution of some free boundary problems

Surface integrals approach to solution of some free boundary problems

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Article ID: iaor1990586
Country: United States
Volume: 1
Start Page Number: 1
End Page Number: 7
Publication Date: May 1988
Journal: Journal of Applied Mathematics and Stochastic Analysis
Authors: , , ,
Abstract:

Inverse problems in which it is required to determine the coefficients of an equation belong to the important class of ill-posed problems. Among these, of increasing significance, are problems with free boundaries. They can be found in a wide range of disciplines including medicine, materials engineering, control theory, etc. The authors apply the integral equations techniques, typical for parabolic inverse problems, to the solution of a generalized Stefan problem. The regularization of the corresponding system of nonlinear integral Volterra equations, as well as local existence, uniqueness, continuation of its solution, and several numerical experiments are discussed.

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