Coefficient Identification Problem for the System of Heat and Wave Equations Associated with a Non-Characteristic Type Change Line

Abstract

The solvability of the inverse problem associated with the search for an unknown coefficient at the lowest term of a mixed parabolic-hyperbolic type equation with a non characteristic line of type change is studied. In the direct problem, we consider an analog of the Tricomi problem for this equation with a nonlocal condition on the characteristics in the hyperbolic part and initial-boundary conditions in the parabolic part of the domain. To determine unknown coefficient, with respect to the solution, defined in the parabolic part of the domain, the integral overdetermination condition is specified. The unique solvability of the inverse problem in the sense of the classical solution is proved.