Nonlocal Problem for a Mixed Type Equation with Singular Coefficient in a Domain Whose Elliptic Part Is a Half-Strip

Abstract

This paper investigates a problem for the Gellerstedt equation with a singular coefficient in a domain whose elliptic part is a vertical half-strip. The elliptic part uses the solution of the Problem $N$ type. By using generalized fractional differentiation operators, we specify a linear combination that relates the value of the solution on characteristics of the equation with the value of the solution and its derivative on the parabolic degeneration line. The uniqueness of the solution of the problem is proved using the extremum principle and the energy integral method. The existence of a solution is proved using the method of integral equations.