Approximate Solution of an Inverse Problem for a Singularly Perturbed Integro-Differential Heat Equation

The paper considers an inverse problem for a singularly perturbed integro-differential heat equation, which consists in determining the boundary condition from additional information on the solution of the initial-boundary value problem. It is proved that an approximate solution of the inverse problem can be obtained by using a finite number of terms in the expansion of the solution of the initial-boundary value problem in a small parameter.