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

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.