A PROBLEM WITH AN INTEGRAL CONDITION FOR A SECOND-ORDER PARABOLIC-HYPERBOLIC EQUATION WITH A LOCAL CONDITION ON THE RIGHT CHARACTERISTIC

This paper considers a boundary value problem for a second-order equation of parabolic-hyperbolic type in a domain consisting of two parts: a parabolic region ang a hyperbolic region. On the right characteristic curve of the hyperbolic part, an integral condition is specified instead of a classical local boundary condition. Using the method of characteristics, the Volterra integral equation theory, and the continuity condition on the type-change line, the existence and uniqueness of the solution are proved. The obtained results generalize classical problems for mixed-type equations with nonlocal boundary conditions.