Nonlocal Boundary-value Problem for Third Order Elliptic-hyperbolic Type Equation
B. I. Islomov, Bakhtiyor Usmonov
Abstract
Abstract In this research work, for a third-order elliptic-hyperbolic type equation, a method for studying a nonlocal boundary-value problem by solving the inverse problem for a second-order mixed elliptic-hyperbolic type equation with an unknown right-hand side was proposed. A new extremume principle for a third-order equation was developed, and with the help of which the uniqueness of the problem is proved. Studying of the existence of solution of the investigated problem, by usingfunctional relations obtained a singular integral equation. Was determined the necessary class of given functions, which provide solvability of the obtained singular equation. Using the general presentation of solution, the solution of the investigated problem is completely constructed in the corresponding domains.