Bifurcation for a free boundary problem modeling the growth of tumors with a drug induced nonlinear proliferation rate

In this paper, we study a free boundary model describing growth of tumors under action of drugs. To our knowledge, in theoretical discussion for free boundary problems, the proliferation rate in tumor models discussed in previous bifurcation results is a linear function of nutrients and inhibitors....

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Bibliographic Details
Published inJournal of Differential Equations Vol. 263; no. 11; pp. 7627 - 7646
Main Authors Li, Fengjie, Liu, Bingchen
Format Journal Article
LanguageEnglish
Published Elsevier Inc 05.12.2017
Subjects
Bifurcation
Existence and uniqueness
Free boundary
Free boundary
92C37
35J60
35B32
Bifurcation
35R35
35K55
Existence and uniqueness
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Summary:In this paper, we study a free boundary model describing growth of tumors under action of drugs. To our knowledge, in theoretical discussion for free boundary problems, the proliferation rate in tumor models discussed in previous bifurcation results is a linear function of nutrients and inhibitors. Whereas in this paper we consider the net proliferation rate as a nonlinear function depending on both nutrients and drugs. First, the existence and the uniqueness of radially symmetric stationary solutions are obtained. Second, we prove that symmetry-breaking solutions bifurcate from the radially symmetric stationary solutions when the concentration of drug on the boundary of tumor is less than one in the rescaled model.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2017.08.023