CLASSICAL SOLUTION OF THE MIXED PROBLEM FOR LINEAR NONSTRICTLY HYPERBOLIC FOURTH-ORDER WITH MULTIPLE CHATACTERISTIC

Author(s):  E. S. Cheb, candidate of Sciences, no, Belorussian State University, Minsk, Republic of Belarus, cheb@bsu.by

E. S. Siminskaya, no, no, Belorussian State University, Minsk, Russia, Slavelena16@gmail.com

Issue:  Volume 52, № 1

Rubric:  Mathematics

Annotation:  In the work is constructed the classical solution of mixed value problem for not strictly hyperbolic homogeneous equation of the fourth order with constant coe cients and the multiple characteristics. We use the method of characteristics to solve this problem. According to this method, general solution of the equation contains the sum of four functions, which are found from initial and boundary conditions. This general solution is constructed for the both cases: with the presence or absence derivatives of lower orders. We obtained matching conditions for initial and boundary conditions. These conditions follow from the requirement of four times continuous differentiability of the solution taking into account smoothness of the functions. A theorem on the existence of a unique classical solution has been proved. The obtained results can be used in the theory of differential equations with partial derivatives and in the computational mathematics.

Keywords:  partial differential hyperbolic equation of the fourth order, initial value problem, boundary value problem, classical solution, method of characteristics, smoothness and matching conditions

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