The existence of a solution to the inverse problem for a single model equation of a mixed parabolic-hyperbolic type: a two-dimensional case

To date, the most comprehensive findings have been achieved in the investigation of direct problems associated with mixed-type equations, yet, the number of works dedicated to solving inverse problems for mixed-type equations is quite limited. Mixed-type equations are applied in nature. A mathematical model of various processes from the field of natural sciences, for example, for modeling the process of gas movement in an enclosed conduit with porous walls, and gas behavior inside the channel is characterized by the wave equation, and in the external domain by the diffusion equation, that is, it is a mixed type equation. This work formulates the inverse problem and prove a theorem on the existence of a solution for one mixed-type PDE serving as a model for parabolic-hyperbolic processes in a two-dimensional parallelepiped domain.