Surface integrals approach to solution of some free boundary problems

Igor Malyshev, Hedley Morris, Vladimir Naroditsky and Leonid Romanyuk

International Journal of Stochastic Analysis, 1988, vol. 1, 1-19

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. We 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.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:956795

DOI: 10.1155/S104895338800022X

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