Xutong Zhao, Mingjun Zhou, Qian Zhou
Abstract:
This article concerns the asymptotic behavior of solutions of
one-dimensional porous medium systems with boundary degeneracy in
bounded and unbounded intervals.
It is shown that the degree of the boundary degeneracy and the exponent
of the nonlinear diffusion determine asymptotic behaviors of solutions.
For the problem in a bounded interval, if the degeneracy is not strong,
the problem admits both nontrivial global and blowing-up solutions,
while if the degeneracy is strong enough,
any nontrivial solution to the problem must blow up in a finite time.
For the problem in an unbounded interval,
the Fujita type blowing-up theorems are established
and the critical Fujita exponent is formulated by
the degree of the boundary degeneracy and the exponent of
nonlinear diffusion.
Submitted April 4, 2022. Published October 28, 2022.
Math Subject Classifications: 35K59, 35B33, 35K65.
Key Words: Porous medium equation; boundary degeneracy; asymptotic behavior.
DOI: https://doi.org/10.58997/ejde.2022.73
Show me the PDF file (353 KB), TEX file for this article.
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Xutong Zhao School of Mathematics Jilin University Changchun 130012, China email: 847692570@qq.com |
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Mingjun Zhou School of Mathematics Jilin University Changchun 130012, China email: zhoumingjun@jlu.edu.cn |
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Qian Zhou School of Mathematics Jilin University Changchun 130012, China email: zhouqian@jlu.edu.cn |
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