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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. (English) Zbl 1250.35117
Summary: 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.
MSC:
35K51Second-order parabolic systems, initial bondary value problems
35R10Partial functional-differential equations
35C10Series solutions of PDE