Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay

Josef Diblík, Denis Khusainov, Oleksandra Kukharenko and Zdeněk Svoboda

Abstract and Applied Analysis, 2012, vol. 2012, 1-27

Abstract:

The first boundary-value problem for an autonomous second-order system of linear partial differential equations of parabolic type with a single delay is considered. Assuming that a decomposition of the given system into a system of independent scalar second-order linear partial differential equations of parabolic type with a single delay is possible, an analytical solution to the problem is given in the form of formal series and the character of their convergence is discussed. A delayed exponential function is used in order to analytically solve auxiliary initial problems (arising when Fourier method is applied) for ordinary linear differential equations of the first order with a single delay.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:219040

DOI: 10.1155/2012/219040

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