Problems with linear initial-boundary conditions for higher order nonlinear hyperbolic equations are investigated. The concept of strong well-posedness of an initial-boundary value problem is introduced, and conditions guaranteeing solvability and strong well-posedness of the problem under consideration are established.
a b s t r a c tFor higher order nonlinear hyperbolic equations nonclassical boundary value problems of Vallée-Poussin type are studied, and unimprovable in a sense sufficient conditions of solvability, unique solvability and well-posedness are established.
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