The Study of Multidimensional Mixed Problem for One Class of Third Order Semilinear Psevdohyperbolic Equations

Abstract

This work is dedicated to the study of existence in small of classical solution of multidimensional mixed problem for one class of third order semilinear psevdohyperbolic equations. Conception of classical solution for mixed problem under consideration is introduced. After applying Fourier method, the solution of original problem is reduced to the solution of some countable system of nonlinear integro-differential equations in unknown Fourier coefficients of the sought solution. Besides, existence theorem in small of classical solution of the mixed problem is proved by contracted mappings principle.