# Article

**Keywords:**

pseudomonotone mapping; radiation effect; inverse problem

**Summary:**

The mathematical analysis of a heat equation and its solutions is a standard part of most textbook of applied mathematics and computational mechanics. However, serious problems from engineering practice do not respect formal simplifications of such analysis, namely at high temperatures, for phase-change materials, etc. This paper, motivated by the material design and testing of a high-temperature thermal accumulator, as a substantial part of the Czech-Swedish project of an original equipment for exploiting solar energy using optical fibres, demonstrates the possibility of both direct and inverse analysis, physically transparent and mathematically correct, paying attention to the set of basic temperature-variable characteristics of thermal transfer.