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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A free boundary problem for a singular system of differential equations: An application to a model of tumor growth


Authors: Shangbin Cui and Avner Friedman
Journal: Trans. Amer. Math. Soc. 355 (2003), 3537-3590
MSC (2000): Primary 34B15; Secondary 35C10, 35Q80, 92C15
Published electronically: May 29, 2003
MathSciNet review: 1990162
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Abstract: In this paper we consider a free boundary problem for a nonlinear system of two ordinary differential equations, one of which is singular at some points, including the initial point $r=0$. Because of the singularity at $r=0$, the initial value problem has a one-parameter family of solutions. We prove that there exists a unique solution to the free boundary problem. The proof of existence employs two ``shooting'' parameters. Analysis of the profiles of solutions of the initial value problem and tools such as comparison theorems and weak limits of solutions play an important role in the proof. The system considered here is motivated by a model in tumor growth, but the methods developed should be applicable to more general systems.


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Additional Information

Shangbin Cui
Affiliation: Institute of Mathematics, Zhongshan University, Guangzhou, Guangdong 510275, People’s Republic of China
Email: mcinst@zsu.edu.cn

Avner Friedman
Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210-1174
Email: afriedman@mbi.osu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03137-4
PII: S 0002-9947(03)03137-4
Keywords: Free boundary problem, stationary solutions, singular differential equations, tumor growth.
Received by editor(s): March 15, 2002
Published electronically: May 29, 2003
Article copyright: © Copyright 2003 American Mathematical Society



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