On exact series solution of strongly coupled mixed parabolic problems (Q2015703)

Summary: This paper studies the construction of the exact solution for parabolic coupled systems of the type \(u_t=Au_{xx}\), \(A1u(0,t)+B_1u_x(0,t)=0\), \(A_2u(l,t)+B_2u_x(l,t)=0\), \(0<x<1\), \(t>0\), and \(u(x,0)=f(x)\), 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.