Approksimatsiya resheniya obratnoy zadachi dlya singulyarno vozmushchennoy sistemy uravneniy v chastnykh proizvodnykh

Abstract

We consider an initial–boundary value problem for a singularly perturbed system of partial differential equations. We pose an inverse problem of determining an unknown initial condition based on additional information about the solution of the initial–boundary value problem. It is proved that using the expansion of the solution of the initial–boundary value problem in the small parameter, one can obtain solutions approximating the solution of the inverse problem with order O(e)or O(e).