Local boundary value problem for one class of third-order equations of elliptic-hyperbolic type

<jats:p>The article studies a local problem for a third-order equation with an elliptic-hyperbolic operator in the principal part. A method is applied that does not require a special representation of the general solution of the equation under consideration. This method determines the study of an elliptic-hyperbolic equation of the second order with unknown right-hand sides, which is of interest for solving important inverse problems of mechanics and physics. Theorems of existence and uniqueness of the classical solution of the problem are proved. The proof is based on the extremum principle for a third-order equation and on the theory of singular, Fredholm integral equations.</jats:p>