On exact series solution for strongly coupled mixed parabolic boundary value problems (Q1724914)

Summary: This paper continues with the construction of the exact solution for parabolic coupled systems of the type \(u_t = A u_{x x}\), \(A_1 u(0, t) + B_1 u_x(0, t) = 0\), \(A_2 u(l, t) + B_2 u_x(l, t) = 0\), \(0 < x < 1\), \(t > 0\), 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. Although this problem has been solved in the literature [the first author et al., ibid. 2013, Article ID 524514, 9 p. (2013; Zbl 1291.35027)], in this work we are using completely new conditions.