ON SOME THREE-DIMENSIONAL VARIANTS OF GOURSAT AND DARBOUX PROBLEMS FOR HIGHER-ORDER HYPERBOLIC EQUATIONS WITH DOMINATING PRINCIPAL PARTS

摘要

Some three-dimensional variants of Goursat and Darboux problems for higher-order hyperbolic equations with dominating principal part are set and investigated. Conditions to the problems' data which in some cases ensure the well-posedness of the problem in question and in other cases, despite the solvability of the problem, imply the presence of an infinite set of linearly independent solutions of corresponding homogeneous problem, are found. We consider both generalized and classical solutions.