On solvability for inverse problem of compact support source determination for the heat equation

Abstract

An inverse problem of reconstructing the source for the heat equations on a plane is considered. As an “overdetermination” (additional information about the solution of the direct problem) a trace of it’s solution is given on a line segment inside of a bounded region. We give sufficient conditions for uniqueness of the solution of the task at hand, prove Fredholm alternative and sufficient conditions for existence and uniqueness of solution of the task. The studying of the problem is performed in the spaces of functions satisfying Hölder condition.