On the formulation and investigation of a boundary value problem for a third-order equation of a parabolic-hyperbolic type

In the paper a novel boundary value problem for a third-order partial differential equation (PDE) of a parabolic-hyperbolic type, within a pentagonal domain consisting of both parabolic and hyperbolic regions was investigated. Such equations are pivotal in modeling complex physical phenomena across diverse fields such as physics, engineering, and finance due to their ability to encapsulate a wide range of dynamics through their mixed-type nature. By employing a constructive solution approach, we demonstrate the unique solvability of the posed problem. The significance of this study lies in its extension of the mathematical framework for understanding and solving higher-order mixed PDEs in complex geometrical domains, thus offering new avenues for theoretical and applied research in mathematical physics and related disciplines.