(untitled) (PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE KYRGYZ REPUBLIC, 2023)
In the field of problems of mathematical physics, various classes of inverse problems associated with partial differential equations have been studied. Among these problems, an important place is occupied by problems where linear and nonlinear Volterra equations of the first and third kind degenerate with solutions in the class of generalized functions, since their studies do not yet have general solution methods. In some cases, research methods have been developed that are related to the regularization method in a generalized sense, having singularities with respect to a small parameter. In this regard, in this article we study the coefficient inverse problem that degenerates into a nonlinear Volterra equation of the first kind with a solution in the class of generalized functions. In many applied problems, there are problems of this type, for example, in problems of moisture transfer in soils, geometric optics, in problems describing the convective diffusion of salts in porous media, etc., which is the relevance of this work.