TY - JOUR
T1 - A regularization of a reaction-diffusion system approximation to the two-phase Stefan problem
AU - Murakawa, Hideki
N1 - Funding Information:
This study was supported in part by the Japan Society for the Promotion of Science and by the Kyushu University 21st Century COE Program, Development of Dynamic Mathematics with High Functionality, of the Ministry of Education, Culture, Sports, Science and Technology of Japan.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/11/15
Y1 - 2008/11/15
N2 - Reaction-diffusion system approximations to the classical two-phase Stefan problem are considered in the present study. A reaction-diffusion system approximation to the Stefan problem has been proposed by Hilhorst et al. from an ecological point of view, and they have given convergence results for the system. In the present study, a new reaction-diffusion system approximation to the Stefan problem is proposed based on regularization of the enthalpy-temperature constitutive relation. For a deeper understanding of the approximation mechanism by means of reaction-diffusion systems, the rates of convergence for both the solutions and the free boundaries are investigated.
AB - Reaction-diffusion system approximations to the classical two-phase Stefan problem are considered in the present study. A reaction-diffusion system approximation to the Stefan problem has been proposed by Hilhorst et al. from an ecological point of view, and they have given convergence results for the system. In the present study, a new reaction-diffusion system approximation to the Stefan problem is proposed based on regularization of the enthalpy-temperature constitutive relation. For a deeper understanding of the approximation mechanism by means of reaction-diffusion systems, the rates of convergence for both the solutions and the free boundaries are investigated.
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U2 - 10.1016/j.na.2007.09.038
DO - 10.1016/j.na.2007.09.038
M3 - Article
AN - SCOPUS:51349134540
VL - 69
SP - 3512
EP - 3524
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 10
ER -