Geodesic
Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors
Shangbin Cui1
1Zhongshan University, Guangzhou, Guangdong, China
Interfaces and free boundaries, Tome 7 (2005) no. 2, pp. 147-159

Voir la notice de l'article provenant de la source EMS Press

DOI

In this paper we study a free boundary problem of a reaction diffusion equation modeling the growth of necrotic tumors. We first reduce this problem into an equivalent initial boundary value problem for a nonlinear parabolic equation on a fixed domain. This parabolic equation is strongly singular in the sense that not only it contains a discontinuous nonlinear function of the unknown function, but also all its coefficients are discontinuous nonlinear functionals of the unknown function. We use approximation method and the Schauder fixed point theorem combined with Lp estimates to prove the existence of a global solution.
DOI : 10.4171/ifb/118
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Free boundary problem, tumor growth, global solution, existence

Shangbin Cui  1

1 Zhongshan University, Guangzhou, Guangdong, China 
Shangbin Cui. Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors. Interfaces and free boundaries, Tome 7 (2005) no. 2, pp. 147-159. doi: 10.4171/ifb/118
@article{10_4171_ifb_118,
     author = {Shangbin Cui},
     title = {Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors},
     journal = {Interfaces and free boundaries},
     pages = {147--159},
     year = {2005},
     volume = {7},
     number = {2},
     doi = {10.4171/ifb/118},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/118/}
}
TY  - JOUR
AU  - Shangbin Cui
TI  - Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors
JO  - Interfaces and free boundaries
PY  - 2005
SP  - 147
EP  - 159
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/118/
DO  - 10.4171/ifb/118
ID  - 10_4171_ifb_118
ER  - 
%0 Journal Article
%A Shangbin Cui
%T Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors
%J Interfaces and free boundaries
%D 2005
%P 147-159
%V 7
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/118/
%R 10.4171/ifb/118
%F 10_4171_ifb_118

Cité par Sources :