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

Abstract EN

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 ( A 1 B 1 A 2 B 2 ) is nonsingular, and A is 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.