Abstract:
The aim of the paper is to investigate the accuracy of the methods for approximate solving a boundary value inverse problem with final overdetermination for a parabolic equation. We use the technique of the continuation to the complex domain and the expansion of the unknown function into a Dirichlet series (exponential series) to formulate the inverse problem as a linear operator equation of the first kind in the appropriate linear normed spaces. This allows us to estimate the continuity module for the inverse problem by means of classical spectral technique and investigate the order-optimal approximate methods for the boundary value inverse problem under study.
Keywords:parabolic equation, boundary value inverse problem, module of continuity of the inverse operator, exponential series.
Fulltext:
PDF file (182 kB)