INITIAL BOUNDARY VALUE PROBLEM FOR THE NON-STRICTLY HYPERBOLIC EQUATION WITH MIXED BOUNDARY CONDITIONS IN A QUADRANT

Abstract

In this paper, the initial boundary value problem for the simplest inhomogeneous second-order non- trictly hyperbolic equation with the mixed Dirichlet and Neumann boundary conditions in a quadrant is fully investigated and solved. By means of the method of characteristics we have obtained its classical solution in analytic explicit form and have proved the necessity and the sufficiency of the established requirements and the smoothness of the original data (the right hand-side of the quation, initial and boundary data) to ensure its unambiguous solvability everywhere in a variety of classical solutions. The requirements on the smoothness of the data of this problem are by “one” are higher than if we have solved the similar first- or secondorder mixed problem for the hyperbolic equation of semi-infinite string vibrations.