Details
| Original language | English |
|---|---|
| Pages (from-to) | 443-457 |
| Number of pages | 15 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 337 |
| Issue number | 1 |
| Publication status | Published - 1 Jan 2008 |
Abstract
This paper is devoted to the study of the bifurcation of a free boundary problem modeling the growth of tumors with the effect of surface tension being considered. The existence of infinitely many branches of bifurcation solutions is proved. The method of analysis is based on reducing the problem to an operator equation in certain Hölder space with a nonlinear Fredholm operator of index 0. The desired result then follows from the Crandall-Rabinowitz bifurcation theorem.
Keywords
- Bifurcation, Free boundary problem, Surface tension, Tumor growth
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of Mathematical Analysis and Applications, Vol. 337, No. 1, 01.01.2008, p. 443-457.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bifurcation for a free boundary problem with surface tension modeling the growth of multi-layer tumors
AU - Zhou, Fujun
AU - Escher, Joachim
AU - Cui, Shangbin
N1 - Funding information: This work on the part of the first and third authors is supported by China National Science Foundation under the grant number 10471157. The third author expresses his sincere thanks for the hospitalities offered by the Institute for Applied Mathematics at the University of Hannover during his visit.
PY - 2008/1/1
Y1 - 2008/1/1
N2 - This paper is devoted to the study of the bifurcation of a free boundary problem modeling the growth of tumors with the effect of surface tension being considered. The existence of infinitely many branches of bifurcation solutions is proved. The method of analysis is based on reducing the problem to an operator equation in certain Hölder space with a nonlinear Fredholm operator of index 0. The desired result then follows from the Crandall-Rabinowitz bifurcation theorem.
AB - This paper is devoted to the study of the bifurcation of a free boundary problem modeling the growth of tumors with the effect of surface tension being considered. The existence of infinitely many branches of bifurcation solutions is proved. The method of analysis is based on reducing the problem to an operator equation in certain Hölder space with a nonlinear Fredholm operator of index 0. The desired result then follows from the Crandall-Rabinowitz bifurcation theorem.
KW - Bifurcation
KW - Free boundary problem
KW - Surface tension
KW - Tumor growth
UR - http://www.scopus.com/inward/record.url?scp=34548276053&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2007.03.107
DO - 10.1016/j.jmaa.2007.03.107
M3 - Article
AN - SCOPUS:34548276053
VL - 337
SP - 443
EP - 457
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -