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Journal of Applied Mathematics and Simulation
Volume 1 (1987), Issue 2, Pages 81-97

On the inverse problem for a heat-like equation

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

Received 5 January 1987; Revised 7 November 1987

Copyright © 1987 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.


Using the integral representation of the solution of the boundary value problem for the equation with one time-dependent coefficient at the highest space-derivative three inverse problems are solved. Depending on the property of the coefficient we consider cases when the equation is of the parabolic type and two special cases of the degenerate/mixed type. In the parabolic case the corresponding inverse problem is reduced to the nonlinear Volterra integral equation for which the uniqueness of the solution is proved. For the special cases explicit formulae are derived. Both “minimal” and overspecified boundary data are considered.