Xinxin Jing, Yuanyuan Nie, Chunpeng Wang
Abstract:
This article concerns the asymptotic behavior of solutions to coupled semilinear parabolic
systems with boundary degeneracy.
For the problem in a bounded domain, it is proved that there exist both nontrivial global
and blowing-up solutions if the degeneracy is not strong,
while any nontrivial solution must blow up in a finite time if the degeneracy is enough strong.
For the problem in an unbounded domain, blowing-up theorems of Fujita type are established.
It is shown that the critical Fujita curve is determined by the strength of degeneracy.
In particular, it is infinite if the degeneracy is enough strong.
Submitted March 19, 2021. Published August 10, 2021.
Math Subject Classifications: 35K65, 35D30, 35B33.
Key Words: Asymptotic behavior; boundary degeneracy.
DOI: https://doi.org/10.58997/ejde.2021.67
Show me the PDF file (341 KB), TEX file for this article.
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Xinxin Jing School of Mathematics Jilin University Changchun 130012, China email: 1776043712@qq.com |
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Yuanyuan Nie School of Mathematics Jilin University Changchun 130012, China email: nieyy@jlu.edu.cn |
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Chunpeng Wang School of Mathematics Jilin University Changchun 130012, China email: wangcp@jlu.edu.cn |
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