Sufficient conditions for reduction of the BVP including a mixed PDE with non‐local boundary conditions to Fredholm integral equations

Abstract

Abstract Physics mathematical equations with three types of hyperbolic, elliptic and parabolic are being used in the design and investigation of physics phenomena and solving engineering and physics mathematical problems. In the extension of this classic theory, Tricomi worked on mixed equation at the prescribed region. In this paper we expand the problem which consists of mixed partial differential equations in the region D with non‐local boundary conditions. First, by using the theory of generalized solutions, we obtain the necessary conditions and then give sufficient conditions for the reduced form of this problem into Fredholm integral equations with weak singularities. In addition, the boundary is expanded to all of the boundary.