Electron. J. Differential Equations, Vol. 2021 (2021), No. 96, pp. 119.
Asymptotic behavior of solutions to porous medium equations with boundary degeneracy
Xutong Zhao, Mingjun Zhou, Xinxin Jing
Abstract:
This article concerns the asymptotic behavior of solutions to a class of
onedimensional 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 blowingup 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 blowingup 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 blowingup 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.
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Xutong Zhao
School of Mathematics
Jilin University
Changchun 130012, China
email: 847692570@qq.com


Mingjun Zhou
School of Mathematics
Jilin University
Changchun 130012, China
email: zhoumingjun@jlu.edu.cn


Xinxin Jing
School of Mathematics
Jilin University
Changchun 130012, China
email: 1776043712@qq.com

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