APPROXIMATE SOLUTION OF THE INVERSE BOUNDARY VALUE PROBLEM FOR A SINGULARLY PERTURBED SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS

The initial boundary value problem for a singularly perturbed system of partial differential equations is considered. The inverse problem is formulated, which consists in determining an unknown boundary condition based on one of the components of the solution given at a fixed point in space. Methods of approximate solution of the inverse problem based on the use of small parameter expansion of the solution of the initial boundary value problem are proposed. Estimates of the accuracy of approximate solutions are obtained. The results of numerical calculations illustrating the accuracy of the proposed methods are presented.