On Some Boundary Value Problems for Nonlinear Degenerate Hyperbolic Equations of Higher Order
نویسنده
چکیده
The Dirichlet problem and other nonclassical boundary value problems for linear hyperbolic equations with two independent variables have been the subject of various studies (see, e.g., [1]–[8], [10]–[16] and the references therein). However such problems for higher order nonlinear hyperbolic equations still remain unstudied. The present paper is an attempt to fulfill the existing gap. Let m and n be natural numbers, 0 < a, b < +∞, Ω = (0, a)×(0, b) and f : Ω×Rmn → R be a continuous function. Consider the nonlinear hyperbolic equation u = f ( x, y, u, . . . , u, . . . , u, . . . , u )
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