Abstract
In this paper, we study the Cauchy problem in a strip for a two-dimensional hyperbolic equation containing the sum of a differential operator and a shift operator acting on a spatial variable that varies over the real axis. An operating scheme is used to construct the solutions of the equation. The solution of the problem is obtained in the form of a convolution of the function found using the operating scheme and the function from the initial conditions of the problem. It is proved that classical solutions of the considered initial problem exist if the real part of the symbol of the differential-difference operator in the equation is positive.
Funder
Ministry of of Science and Higher Education of the Russian Federation
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference16 articles.
1. Pinney, E. (1958). Ordinary Difference-Differential Equations, University of California Press.
2. Bellman, R., and Cooke, K.L. (1963). Differential-Difference Equations, Academic Press.
3. Hale, J. (1977). Theory of Functional-Differential Equations, Springer.
4. Kuang, Y. (1993). Delay Differential Equations with Applications in Population Dinamics, Academic Press.
5. Some difference-differential equations containing both advance and retardiation;Schulman;J. Math. Phys.,1974
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献