ABOUT SOLUTIONS IN THE BROAD SENSE OF NONLINEAR SYSTEMS IN PARTIAL DERIVATIVES OF THE FIRST ORDER - Bekbauova А. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2025)
The article addresses the issues of existence and uniqueness of periodic solutions in some variables in the generalized sense for a nonlinear system of first-order partial differential equations. Mathematical models of physical and other processes are described using partial differential equations. The article provides definitions of solutions in the generalized sense for a nonlinear system of first-order partial differential equations, as well as the main properties of the differentiation operator. The method of characteristics and the method of contraction mappings are applied. The theorem on the existence and uniqueness of a periodic solution in some variables in the generalized sense for a nonlinear system of first-order partial differential equations is proven within a ball. The necessary and sufficient conditions for periodicity in some variables of the solution in the generalized sense are also proven.