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Journal of Applied Mathematics and Simulation
Volume 1 (1988), Issue 4, Pages 305-323

Surface integrals approach to solution of some free boundary problems

Department of Mathematics and Computer Science, San Jose State University, San Jose 95192, CA, USA

Received 3 November 1988; Revised 21 December 1988

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.