Boundary value problems for a model hyperbolic equation of the third order with non-local conditions of the first kind

Considers nonlocal problems of the first kind for a model third-order hyperbolic equation. The main goal of the article is to prove the solvability of nonlocal problems of the first kind for a model third-order hyperbolic equation. Using the Riemann function method, the problem is reduced to Volterra integral equations of the second kind. Using the method of integral equations, the existence of a unique solution to nonlocal problems of the first kind is proven. The resulting solution to nonlocal problems of the first kind makes it possible to describe the process of moisture transfer in soils, heat transfer in a heterogeneous medium, and fluid filtration in porous media.