ПОНЯТИЕ ПРЯМОЙ И ОБРАТНОЙ ЗАДАЧИ В МАТЕМАТИЧЕСКОЙ ФИЗИКЕ - Меражова, Ш.Б. (SCIENCE and SOCIETY, 2020)
The article analyzes the formulation and solution of several direct problems and inverse problems for the equations of mathematical physics. In the subject’s program, they mainly study the direct problems posed to the equations of mathematical physics. Inverse problems are widely applied, therefore, students should be familiar with this concept when studying subjects: “Partial differential equation”, “Equations of mathematical physics”and in future they can apply them in their scientific activities. In this article we briefly talked about direct and inverse problems and analyzed several direct problems and inverse problems Also in this paper inverse problems for model equation of mixed parabolic – hyperbolic type are considered. The solutions of these problems are obtained for one-dimensional case in a rectangular domain. So we state the inverse problem for an integro-differential equation of parabolic type with an integral term on convolution type,i.e., inverse problem of determining in one integro-differential equation of parabolic type.
Keywords: direct problems; inverse problems; initial conditions; boundary conditions; characteristic system of equations; general solution; particular solution; equations of parabolic type; integral equations; core of the integral equation