scholarly journals On the Exact Series Solution for Nonhomogeneous Strongly Coupled Mixed Parabolic Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Vicente Soler ◽  
Emilio Defez ◽  
Roberto Capilla ◽  
José Antonio Verdoy
Keyword(s):  
Boundary Value Problems ◽  
Series Solution ◽  
Boundary Value ◽  
Block Matrix ◽  
Coupled Systems ◽  
Parabolic Boundary ◽  
Strongly Coupled ◽  
Parabolic Boundary Value Problems ◽  
Stable Matrix

An exact series solution for nonhomogeneous parabolic coupled systems of the typeut-Auxx=Gx, t, A1u0, t+B1ux0, t=0, A2ul, t+B2uxl, t=0, 0<x<1, t>0, ux, 0=fx, whereA1, A2, B1, andB2are arbitrary matrices for which the block matrix is nonsingular, andAis a positive stable matrix, is constructed.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vicente Soler ◽  
Emilio Defez ◽  
José Antonio Verdoy
Keyword(s):  
Exact Solution ◽  
Boundary Value Problems ◽  
Series Solution ◽  
Boundary Value ◽  
Block Matrix ◽  
Coupled Systems ◽  
Parabolic Boundary ◽  
Strongly Coupled ◽  
Parabolic Boundary Value Problems ◽  
Stable Matrix

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.

scholarly journals On Exact Series Solution of Strongly Coupled Mixed Parabolic Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Vicente Soler ◽  
Emilio Defez ◽  
M. V. Ferrer ◽  
J. Camacho
Keyword(s):  
Exact Solution ◽  
Series Solution ◽  
Block Matrix ◽  
Coupled Systems ◽  
Parabolic Problems ◽  
Strongly Coupled ◽  
Stable Matrix

This paper studies the construction of the exact solution for parabolic coupled systems of the type , , , , , and , where , , , and are arbitrary matrices for which the block matrix is nonsingular, and is a positive stable matrix.

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