Remarks to the Computational Analysis of Semilinear Direct and Inverse Problems of Heat Transfer

摘要

Recent methods of numerical analysis of both direct and inverse heat transfer problems combine the partial knowledge of analytical or semianalytical solutions with advanced computational algorithms. Numerous approaches rely on the engineering experience with linear or ad hoc linearized initial and boundary value formulations, together with their incomplete experimental validation, avoiding their proper non-trivial mathematical verification. This paper demonstrates typical difficulties of such verification for a direct and inverse variant of a model problem of heat conduction with temperature-dependent thermal conductivity and diffusivity, together with comments to potential generalizations and practical applications of its results.