On the exact series solution for nonhomogeneous strongly coupled mixed parabolic boundary value problems (Q1725078)

Summary: An exact series solution for nonhomogeneous parabolic coupled systems of the type \(u_t - A u_{x x} = G \left(x, t\right), A_1 u \left(0, t\right) + B_1 u_x \left(0, t\right) = 0, A_2 u \left(l, t\right) + B_2 u_x \left(l, t\right) = 0, 0 < x < 1, t > 0, u \left(x, 0\right) = f \left(x\right)\), where \(A_1, A_2, B_1\), and \(B_2\) are arbitrary matrices for which the block matrix \(\begin{pmatrix} A_1 & B_1 \\ A_2 & B_2 \end{pmatrix}\) is nonsingular, and \(A\) is a positive stable matrix, is constructed.