| Issue |
Wuhan Univ. J. Nat. Sci.
Volume 29, Number 2, April 2024
|
|
|---|---|---|
| Page(s) | 95 - 105 | |
| DOI | https://doi.org/10.1051/wujns/2024292095 | |
| Published online | 14 May 2024 | |
Mathematics
CLC number: O175
Blow-up for a Porous Medium Equation with Local Linear Boundary Dissipation
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China
† Corresponding author. E-mail: 1070099@hnust.edu.cn
Received:
15
September
2023
This article investigates the blow-up behaviors for a porous medium equation with a superlinear source and local linear boundary dissipation. Making use of the concavity method, we establish sufficient conditions to guarantee the occurrence of the finite time blow-up phenomenon. Meanwhile, we show the existence of the finite time blow-up solutions for arbitrarily high initial energy. Finally, we derive the life span bounds (i.e., the lower and upper bounds of the blow-up time).
Key words: porous medium equation / blow-up behavior / life span bounds
Cite this article: YANG Jichen, LIU Dengming. Blow-up for a Porous Medium Equation with Local Linear Boundary Dissipation[J]. Wuhan Univ J of Nat Sci, 2024, 29(2): 95-105.
Biography: YANG Jichen, male, Master candidate, research direction: differential equations and their applications. E-mail: 2193822875@qq.com
Fundation item: Supported by Scientific Research Fund of Hunan Provincial Education Department (23A0361)
© Wuhan University 2024
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