Electron. J. Differential Equations,
Vol. 2016 (2016), No. 330, pp. 116.
Global fast and slow solutions of a singlespecies bacillus system
with free boundary
Youpeng Chen, Xingying Liu, Lei Shi
Abstract:
In this article, we consider a free boundary problem for a reaction diffusion
equation which describes the dynamics of single bacillus population in higher
space dimensions and heterogeneous environment. For simplicity, we assume
that the environment and solution are radially symmetric.
First, by using the contraction mapping theorem, we prove that the local solution
exists and is unique. Then, some sufficient conditions are given under which
the solution will blow up in finite time. Our results indicate that the
blowup occurs if the initial data are sufficiently large. Finally, the long time
behavior of the global solution is discussed. It is shown that the global
fast solution does exist if the initial data are sufficiently small,
while the global slow solution is possible if the initial data are suitably large.
Submitted March 15, 2016. Published December 27, 2016.
Math Subject Classifications: 35B40, 35K57, 35K60, 35K65.
Key Words: Reactiondiffusion; free boundary; global fast solution;
global slow solution; blowup.
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Youpeng Chen
School of Mathematics
Yancheng Normal University
Yancheng 224002, China
email: youpengc123@aliyun.com


Xingying Liu
School of Mathematics
Yancheng Normal University
Yancheng 224002, China
email: 1220572745@qq.com


Lei Shi
College of Science
Nanjing Agricultural University
Nanjing 210095, China
email: shileijsxh@163.com

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