On Exact Series Solution of Strongly Coupled Mixed Parabolic Problems

Abstract

This paper studies the construction of the exact solution for parabolic coupled systems of the type $u_t=A{u}_{xx}$, $A_{\mathrm{1}}u(\mathrm{0},t)+B_{\mathrm{1}}{u}_x(\mathrm{0},t)=\mathrm{0}$, $A_{\mathrm{2}}u(l,t)+B_{\mathrm{2}}{u}_x(l,t)=\mathrm{0}$, , $t>\mathrm{0}$, and $u(x,\mathrm{0})=f(x)$, where $A_1$, $A_2$, $B_1$, and $B_2$ are arbitrary matrices for which the block matrix is nonsingular, and $A$ is a positive stable matrix.