Abstract:

This article discusses the problem of determining two unknown coefficients in one multidimensional quasilinear parabolic equation. By means of overdetermination conditions, the initial inverse problem is reduced to the direct auxiliary Cauchy problem. Furthermore, using the weak approximation method, on the basis of sufficiently smooth input data, the solvability of the direct problem is established. The solution of the inverse problem is written out explicitly through the solution of a direct problem, on this basis, the existence and uniqueness theorem of the solution of the original inverse problem in the class of smooth bounded functions is proved. An example of input data satisfying the conditions of the theorem is given.