Localization of the discontinuity line of the right-hand side of a differential equation

Abstract

We propose a new approach to studying the inverse problems for differential equations with constant coefficients. Its application is illustrated by an example of some partial differential equation with three independent variables. The right-hand side of the equation is assumed to be a function discontinuous in spatial variables. In the inverse problem, it is required to find some hull containing the discontinuity line of the right-hand side. An algorithm for constructing such a hull is obtained: It is a square whose sides are tangent to the discontinuity line.