A. Ya. Dorogovtsev, O. Yu. Trofimchuk, "On the stability of stationary solutions of a linear integro-differential equation", International Journal of Stochastic Analysis, vol. 14, Article ID 265389, 12 pages, 2001. https://doi.org/10.1155/S1048953301000107
On the stability of stationary solutions of a linear integro-differential equation
In this paper the following two connected problems are discussed. The problem of the existence of a stationary solution for the abstract equation containing a small parameter in Banach space is considered. Here is a fixed operator, and is a stationary process. The asymptotic expansion of the stationary solution for equation (1) in the series on degrees of e is given.We have proved also the existence of a stationary with respect to time solution of the boundary value problem in for a telegraph equation (6) containing the small parameter . The asymptotic expansion of this solution is also obtained.
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