SOLUTION OF MULTIDIMENSIONAL INVERSE PROBLEM FOR THIRD-ORDER DIFFERENTIAL EQUATION
In this paper, we investigate a multidimensional inverse problem for third order nonlinear differential equations in an unbounded domain. Based on the auxiliary function method, the problem under study is transformed to Burgers type problem, and the transformed problem under study reduces to the first kind Volterra type integral equation, which is the relevance of this work. Note that the investigated problems in physical meaning are included in the class of problems of wave theory. For example, in particular, under certain restrictions, the problem under consideration generalizes the planar Lame problem.
inverse problem, Cauchy problem, fixed parameter, smooth functions, Volterra equations of the first and third kind, regularizing algorithms.