一类抛物方程爆破时间下界的确定方法与有效性分析

数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1033-1040.

一类抛物方程爆破时间下界的确定方法与有效性分析

覃思乾,凌征球*(),周泽文

玉林师范学院数学与统计学院广西玉林 537000

收稿日期:2018-09-05 出版日期:2019-10-26 发布日期:2019-11-08
通讯作者: 凌征球 E-mail:lingzq00@163.com
基金资助:
国家自然科学基金(11461076)

Some Methods for Determining the Lower Bound of Blow-up Time in a Parabolic Problem and Effectiveness Analysis

Siqian Qin,Zhengqiu Ling*(),Zewen Zhou

School of Mathematics and Statistics, Yulin Normal University, Guangxi Yulin 537000

Received:2018-09-05 Online:2019-10-26 Published:2019-11-08
Contact: Zhengqiu Ling E-mail:lingzq00@163.com
Supported by:
the NSFC(11461076)

摘要/Abstract

摘要：

利用能量估计方法与微分不等式技术，该文研究了一类具有可变非局部源项的牛顿渗流方程的Neumann边界值问题解的爆破现象，给出了解发生爆破时两个估计爆破时间下界的方法以及它们的有效性分析.

关键词: 牛顿渗流方程, 可变源, 爆破, 下界, 有效性

Abstract:

In this paper, we consider the blow-up phenomenon to a type of Newtonian filtration equation with variable source subject to homogeneous Neumann boundary condition. We give two methods to determine the lower bound for blow-up time of solution in $\Omega \in {{\mathbb{R}}^{3}}$ if the solutions blow up by energy estimation method and diferential inequality technique. Moreover, the effectiveness of these methods are also discussed.

Key words: Newtonian filtration equation, Variable source, Blow-up, Lower bound, Effectiveness

中图分类号:

O175.2

覃思乾,凌征球,周泽文. 一类抛物方程爆破时间下界的确定方法与有效性分析[J]. 数学物理学报, 2019, 39(5): 1033-1040.

Siqian Qin,Zhengqiu Ling,Zewen Zhou. Some Methods for Determining the Lower Bound of Blow-up Time in a Parabolic Problem and Effectiveness Analysis[J]. Acta mathematica scientia,Series A, 2019, 39(5): 1033-1040.

参考文献 11

1	Quittner R, Souplet P. Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States. Basel: Birkhauser, 2007
2	Straughan B. Explosive Instabilities in Mechamics. Berlin: Springer-Verlag, 1998
3	Payne L E , Schaefer P W . Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. J Math Anal Appl, 2007, 328: 1196- 1205 doi: 10.1016/j.jmaa.2006.06.015
4	Payne L E , Philippin G A , Schaefer P W . Bounds for blow-up time in nonlinear parabolic problems. J Math Anal Appl, 2008, 338: 438- 447 doi: 10.1016/j.jmaa.2007.05.022
5	Payne L E , Philippin G A , Schaefer P W . Blow-up phenomena for some nonlinear parabolic problems. Nonlinear Anal, 2008, 69: 3495- 3502 doi: 10.1016/j.na.2007.09.035
6	Liu D M , Mu C L , Xin Q . Lower bounds estimate for the blow-up time of a nonlinear nonlocal porous medium equation. Acta Math Sci, 2012, 32B (3): 1206- 1212
7	Song X F , Lv X S . Bounds of blowup time and blowup rate estimates for a type of parabolic equations with weighted source. Appl Math & Computation, 2014, 236: 78- 92
8	Baghaei K , Hesaaraki M B . Lower bounds for the blow-up time of nonlinear parabolic problems with Robin boundary conditions. Electron J Differential Equations, 2014, 113: 1- 5
9	马羚未, 方钟波. 具有加权非局部源和Robin边界条件的反应-扩散方程解的爆破时间下界. 数学物理学报, 2017, 37A (1): 146- 157 doi: 10.3969/j.issn.1003-3998.2017.01.014
	Ma L W , Fang Z B . Lower bounds of blow-up time for a reaction-diffusion equation with weighted nonlocal sources and Robin type boundary conditions. Acta Math Sci, 2017, 37A (1): 146- 157 doi: 10.3969/j.issn.1003-3998.2017.01.014
10	Baghaei K , Ghaemi M B , Hesaaraki M . Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source. Appl Math Letters, 2014, 27: 49- 52 doi: 10.1016/j.aml.2013.07.012
11	Payne L E , Schaefer P W . Lower bounds for blow-up time in parabolic problems under Neumann conditions. Appl Anal, 2006, 85: 1301- 1311

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