Dirichlet–Neumann problem for system of weakly nonlinear hyperbolic equations of high order with constant coefficients

Abstract

In the region, which is a Cartesian product of the interval on the unit circle, the boundary value problem with Dirichlet–Neumann conditions in the time variable and the conditions of 2π-periodicity in the spatial coordinate for the system of weakly nonlinear hyperbolic equations of high order with constant coefficients has been investigated. The Banach–Caccioppoli fixed-point theorem has been applied and the conditions for unique solvability for the problem in Sobolev spaces have been established. Cite as: S. M. Repetylo, M. M. Symotiuk, “Dirichlet–Neumann problem for system of weakly nonlinear hyperbolic equations of high order with constant coefficients,” Prykl. Probl. Mekh. Mat. , Issue 17, 105–112 (2019) (in Ukrainian), https://doi.org/10.15407/apmm2019.17.105-112