Uniqueness of determination of a source function in a quasilinear inverse Stefan problem with final observation
The author considers the inverse Stefan problem for the case where thermal coefficients are functions of time, position and temperature. The model consists of a one dimensional body of given length subject to change of phase. The problem is to find the temperature field in the given domain, the phase transition depending on time and the source function of initial functions, which are assumed to be given in direct Stefan problems. Also, the goal is to derive sufficient conditions ensuring the uniqueness of determining an unknown source in a quasi-linear inverse Stefan problem with additional information in the form of overdetermination. For such a problem, the author found the conditions imposed on the input data of the inverse Stefan problem, the uniqueness of a solution, and a class of admissible solutions of the inverse Stefan problem.
scientific article; zbMATH DE number 6106474