On Exact Series Solution for Strongly Coupled Mixed Parabolic Boundary Value Problems

This paper continues with the construction of the exact solution for parabolic coupled systems of the typeut=Auxx,A1u(0,t)+B1ux(0,t)=0,A2u(l,t)+B2ux(l,t)=0,0<x<1,t>0, andu(x,0)=f(x), whereA1,A2,B1, andB2are arbitrary matrices for which the block matrix(A1B1A2B2)is nonsingular, andAis a positive stable matrix. Although this problem has been solved in the literature (Soler et al., 2013), in this work we are using completely new conditions.