Unknown coefficient problem for mixed equation of parabolic-hyperbolic type with non-local boundary conditions on characteristics

Abstract

For an equation of a mixed parabolic-hyperbolic type with a characteristic line of type change, we study the inverse problem associated with the search for an unknown coefficient at the lowest term of the parabolic equation. 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 the Dirichlet condition in the parabolic part of the domain. In order to determine the unknown coefficient by the solution on the parabolic part of the domain, the integral overdetermination condition is proposed. Global results on the unique solvability of the inverse problem in the sense of the classical solution are proved.