Xutong Zhao, Mingjun Zhou, Xinxin Jing
Abstract:
This article concerns the asymptotic behavior of solutions to a class of
one-dimensional porous medium equations with boundary degeneracy on bounded and
unbounded intervals.
It is proved that the degree of degeneracy, the exponents of the nonlinear diffusion,
and the nonlinear source affect the asymptotic behavior of solutions.
It is shown that on a bounded interval, the problem admits both nontrivial global
and blowing-up solutions if the degeneracy is not strong;
while any nontrivial solution must blow up if the degeneracy is strong enough.
For the problem on an unbounded interval, the blowing-up theorems of Fujita type
are established. The critical Fujita exponent is finite if the degeneracy
is not strong, while infinite if the degeneracy is strong enough.
Furthermore, the critical case is proved to be the blowing-up case if it is finite.
Submitted May 29, 2021. Published December 3, 2021.
Math Subject Classifications: 35K59, 35B33, 35K65.
Key Words: Critical Fujita exponent; porous medium equation;
boundary degeneracy.
Show me the PDF file (354 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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Xinxin Jing School of Mathematics Jilin University Changchun 130012, China email: 1776043712@qq.com |
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