TY - JOUR
T1 - Boundary value problems for the Cimmino system via quaternionic analysis
AU - Abreu Blaya, Ricardo
AU - Bory Reyes, Juan
AU - Guzmán Adán, Alí
AU - Schneider, Baruch
PY - 2012/12/15
Y1 - 2012/12/15
N2 - In this paper, we study a class of boundary value problems for a first order linear partial differential equation (all of whose solutions are harmonic functions), which is called the Cimmino system. With the help of the one-to-one correspondence between the theory of quaternion valued hyperholomorphic functions and that of Cimmino system's solutions, necessary and sufficient conditions for the solvability of the non-homogeneous Cimmino system coupled by the boundary conditions are derived and its general solution is explicitly described.
AB - In this paper, we study a class of boundary value problems for a first order linear partial differential equation (all of whose solutions are harmonic functions), which is called the Cimmino system. With the help of the one-to-one correspondence between the theory of quaternion valued hyperholomorphic functions and that of Cimmino system's solutions, necessary and sufficient conditions for the solvability of the non-homogeneous Cimmino system coupled by the boundary conditions are derived and its general solution is explicitly described.
KW - Boundary value problems
KW - Cimmino system
KW - Quaternionic analysis
UR - http://www.scopus.com/inward/record.url?scp=84870055319&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2012.10.022
DO - 10.1016/j.amc.2012.10.022
M3 - Artículo
SN - 0096-3003
VL - 219
SP - 3872
EP - 3881
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 8
ER -