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Analytic solution of mixed problems for the generalized diffusion equation with delay. (English) Zbl 1062.35157

Summary: This paper deals with the construction of the exact series solution of mixed problems related to the generalized diffusion equation \[ u_t(t,x)=a^2 u_{xx}(t,x)+b^2u_{xx}(t-\tau,x),\;t>\tau,\;0\leq x\leq l. \] A separation of variables method is used to develop an exact theoretical series solution, which can be truncated to obtain a continuous numerical solution with prescribed accuracy in bounded domains.

MSC:

35R10 Partial functional-differential equations
35C10 Series solutions to PDEs
76R50 Diffusion
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