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: | Malyshev Igor, Morris Hedley, Naroditsky Valdimir, Romanyuk Leonid. |
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.