Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle |
| |
Authors: | A T Assanova |
| |
Institution: | 1.Institute of Mathematics and Mathematical Modeling,Ministry of Education and Science,Almaty,Republic of Kazakhstan |
| |
Abstract: | We consider a nonlocal problem with integral conditions for a system of hyperbolic equations in rectangular domain. We investigate the questions of existence of unique classical solution to the problemunder consideration and approaches of its construction. Sufficient conditions of unique solvability to the investigated problem are established in the terms of initial data. The nonlocal problem with integral conditions is reduced to an equivalent problem consisting of the Goursat problem for the system of hyperbolic equations with functional parameters and functional relations. We propose algorithms for finding a solution to the equivalent problem with functional parameters on the characteristics and prove their convergence. We also obtain the conditions of unique solvability to the auxiliary boundary-value problem with an integral condition for the system of ordinary differential equations. As an example, we consider the nonlocal boundary-value problem with integral conditions for a two-dimensional system of hyperbolic equations. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|