| Abstract: |
| In the present communication we study a questions for existence and uniqueness of solution to the boundary value problem for the system of hyperbolic partial differential equations with discrete effect memory on the rectangular domain.
Considered problem is transferred to family of problems for differential equations with discrete effect memory and integral condition by introducing a new functions.
Further, introducing functional parameters as the values of the desired solution along the lines of the domain partition with respect to the time variable, we obtain an equivalent problem for the system of differential equations with initial conditions and functional relations with respect to the introduced parameters. We have developed a two-stage procedure to approximately solve the latter problem. We have obtained some conditions for the convergence of approximate solutions to the exact solution of the problem under study in terms of input data and proved that these conditions guarantee the existence of a unique solution of the equivalent problem. Finally, we have established coefficient conditions for the unique solvability of the problem for the system of hyperbolic partial differential equations with discrete effect memory
subject initial and integral conditions.
This research is funded by the Science Committee of the Ministry of Science and Higher Education of Republic of Kazakhstan (Grant no. AP19675193). |
|