Exact solution of coupled mixed diffusion problems with coupled boundary conditions

In this paper, existence conditions and construction of an exact series solution for coupled diffusion problems of the type ut — Auxx = G(x,t), u(0,t) = 0, Bu(1,t) + Cux(1,t) = 0, u(x,0) = ƒ(x), 0 ≤ x ≤ 1, t > 0 are treated. HereA is a positive stable matrix, matrix C−1B has real eigenvalues, and no diagonalizable hypothesis on these matrices is assumed.