REGULARIZATION OF THE ALLER TYPE INVERSE PROBLEM, WHERE NONLINEAR VOLTERRA EQUATION OF THE FIRST KIND WITH A SPECIAL SOLUTION IS DEGENERATES (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, animportant place is occupied by problems where linear and nonlinear Volterra equations of the firstand third kind degenerate with solutions in the class of generalized functions, since their studiesdo not yet have general solution methods. In some cases, research methods have been developedthat 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 problemthat degenerates into a nonlinear Volterra equation of the first kind with a solution in the class ofgeneralized functions. In many applied problems, there are problems of this type, for example, inproblems of moisture transfer in soils, geometric optics, in problems describing the convectivediffusion of salts in porous media, etc., which is the relevance of this work.
Keywords: Differential equations, Volterra integral equations, ill-posed inverse problem, method of integral operators, regularization method.