We consider the problem of determining the conductivity in a heat equation from overspecified non-smooth data. It is an ill-posed inverse problem. We apply a regularization approach to define and construct a stable approximate solution. We also conduct numerical simulation to demonstrate the accuracy of our approximation.
Based on the approximate solution of the dispersion equation, the paper presents an analysis of the system of dynamic thermoelasticity equations taking into account the generalized heat equation. It is noted that during the wave process of heat transfer, a sufficiently intensive process of energy exchange between thermal and elastic fields is realized, while depending on the relations of the characteristic relaxation times, the direction of energy exchange can change.
Some possible options for the formulation of inverse problems are considered. The ultimate research goals in these cases determine the algorithms for the approximate solution of the inverse problem and allow one to correctly interpret these solutions. Two main statements of inverse problems considered: inverse problems of synthesis and inverse problems of measurement. It is shown that in inverse synthesis problems one should not take into account the error of the mathematical model. In addition, it is possible in these cases to synthesize approximate solution algorithms that do not have a regularizing property. Examples of practical problems considered.
Determination of conductivity in a heat equation
