一类抛物方程爆破时间下界的确定方法与有效性分析

Abstract

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

CLC Number:

O175.2

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.

Trendmd

References 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

Metrics

Viewed

Full text

145

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	0	0	0	145

From	Others	local

Times	3	142
Rate	2%	98%

Abstract

Just accepted	Online first	Issue

0	0	67

	From	Others

	Times	67
	Rate	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

[1]	Yafeng Li,Qiao Xin,Chunlai Mu. The Discrete Possion Equation and the Heat Equation with the Exponential Nonlinear Term [J]. Acta mathematica scientia,Series A, 2019, 39(4): 773-784.
[2]	Qunfei Long,Jianqing Chen. Blow-Up Phenomena of Solutions for a Class of Viscous Cahn-Hilliard Equation with Gradient Dependent Potentials and Sources [J]. Acta mathematica scientia,Series A, 2019, 39(3): 510-517.
[3]	Ting Ji,Lianggen Hu,Jing Zeng. The Non-Existence of Non-Radial Blow-Up Solutions for the Quasilinear Elliptic System [J]. Acta mathematica scientia,Series A, 2019, 39(2): 307-315.
[4]	Zhaoyang Shang. Blow-Up Criterion for Incompressible Magnetohydrodynamics Equations in Besov Space [J]. Acta mathematica scientia,Series A, 2019, 39(1): 67-80.
[5]	Yijun He,Huaihong Gao,Hua Wang,Shunyong Li. A Note on Global Solution and Blow-Up for a Class of Pseudo p-Laplacian Evolution Equations with Logarithmic Nonlinearity [J]. Acta mathematica scientia,Series A, 2019, 39(1): 125-132.
[6]	Baoyan Sun. Lower Bound of Blow-Up Time for a p-Laplacian Equation with Nonlocal Source [J]. Acta mathematica scientia,Series A, 2018, 38(5): 911-923.
[7]	Zhao Yuanzhang, Ma Xiangru. Blow-Up Analysis for a Nonlocal Reaction-Diffusion Equation with Variant Diffusion Coefficient [J]. Acta mathematica scientia,Series A, 2018, 38(4): 750-769.
[8]	Liu Dengming, Zeng Xianzhong, Mu Chunlai. A Blow-up Result for a Higher-Order Damped Hyperbolic System with Nonlinear Memory Terms [J]. Acta mathematica scientia,Series A, 2018, 38(2): 304-312.
[9]	Su Xiao, Wang Shubin. Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1085-1093.
[10]	Ma Lingwei, Fang Zhongbo. Lower Bounds of Blow-up Time for a Reaction-Diffusion Equation with Weighted Nonlocal Sources and Robin Type Boundary Conditions [J]. Acta mathematica scientia,Series A, 2017, 37(1): 146-157.
[11]	Liu Yang. Potential Well and Application to Non-Newtonian Filtration Equations at Critical Initial Energy Level [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1211-1220.
[12]	Yang Lingyan, Li Xiaoguang, Chen Ying. A Sharp Threshold of Blow-Up of a Class of Schrödinger-Hartree Equations [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1117-1123.
[13]	Ling Zhengqiu, Wang Zejia. Blow-Up Questions of Solutions to a Class of p-Laplace Equation with Dissipative Gradient Term [J]. Acta mathematica scientia,Series A, 2016, 36(5): 958-964.
[14]	Bian Dongfen, Tang Tong. Blow-Up of Smooth Solutions to the Compressible MHD Equations [J]. Acta mathematica scientia,Series A, 2016, 36(4): 715-721.
[15]	He Yue. New Estimates of Lower Bound for the First Eigenvalue on Compact Manifolds with Positive Ricci Curvature [J]. Acta mathematica scientia,Series A, 2016, 36(2): 215-230.

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

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 11

Related Articles 15

Metrics

Comments

Recommended 10