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 -