Rocky Mountain Journal of Mathematics

Global asymptotic stability of positive steady states of a solid avascular tumor growth model with time delays

Shihe Xu and Fangwei Zhang

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Abstract

In this work, global stability of a free boundary problem modeling solid avascular tumor growth is studied. The model is considered with time delays during the proliferation process. We prove that the unique positive constant steady state is globally asymptotically stable under some assumptions. The proof uses the comparison principle and the iteration method.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 5 (2018), 1685-1702.

Dates
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1539936041

Digital Object Identifier
doi:10.1216/RMJ-2018-48-5-1685

Mathematical Reviews number (MathSciNet)
MR3866564

Zentralblatt MATH identifier
06958797

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations 92B05: General biology and biomathematics

Keywords
Solid avascular tumor parabolic equations global solution global asymptotic stability

Citation

Xu, Shihe; Zhang, Fangwei. Global asymptotic stability of positive steady states of a solid avascular tumor growth model with time delays. Rocky Mountain J. Math. 48 (2018), no. 5, 1685--1702. doi:10.1216/RMJ-2018-48-5-1685. https://projecteuclid.org/euclid.rmjm/1539936041


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