An analogue of the Darboux problem for hyperbolic equations of the third order in a rectangular triangular domain

The article considers the Darboux problem for a third-order hyperbolic equation in a rectangular triangular domain. The main purpose of the article is to prove the solvability of the Darboux problem. Using the Riemann function method, the problem is reduced to Volterra integral equations of the second kind. The existence of a unique solution to the Darboux problem is proved by the method of integral equations. The obtained solution of the Darboux problem allows us to describe the process of moisture transfer in soils, heat transfer in a heterogeneous medium, and liquid filtration in porous media.