Blow-Up Phenomenon for a Reaction-Diffusion Equation with Weighted Nonlocal Gradient Absorption Terms

被引：3

作者：

Liang, Mengyang ^{[1
]}

Fang, Zhong Bo ^{[1
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2021年 / 18卷 / 04期

关键词：

Reaction-diffusion equation; Weighted nonlocal gradient absorption terms; Blow-up time; Upper bound; Lower bound; 35K92; 35B33; 35B40; PARABOLIC EQUATIONS; LOWER BOUNDS; TIME; NONLINEARITY;

D O I：

10.1007/s00009-021-01795-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the blow-up phenomenon of solutions to a reaction-diffusion equation with weighted nonlocal gradient absorption terms in a bounded domain. Based on the method of auxiliary function and the technique of modified differential inequality, we establish appropriate conditions on weight function and nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, upper and lower bounds for blow-up time are derived under appropriate measure in higher dimensional spaces.

引用

页数：19

共 23 条

[1] The local theory for viscous Hamilton-Jacobi equations in Lebesgue spaces [J].

Ben-Artzi, M ;

Souplet, P ;

Weissler, FB .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (04) :343-378

[2]

Brezis H, 2011, UNIVERSITEXT, P1

[3] Lower Bounds Estimate for the Blow-Up Time of a Slow Diffusion Equation with Nonlocal Source and Inner Absorption [J].

Fang, Zhong Bo ;

Yang, Rui ;

Chai, Yan .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2014, 2014

[4] The Cauchy problem for ut = UDELTAu+|delu|q [J].

Gilding, BH ;

Guedda, M ;

Kersner, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 284 (02) :733-755

[5] Blow-up of positive solutions for a family of nonlinear parabolic equations in general domain in RN [J].

Hesaaraki, M ;

Moameni, A .

MICHIGAN MATHEMATICAL JOURNAL, 2004, 52 (02) :375-389

[6] Blow up Theories for Semilinear Parabolic Equations [J].

Hu, Bei .

BLOW UP THEORIES FOR SEMILINEAR PARABOLIC EQUATIONS, 2011, 2018 :1-+

[7] NONEXISTENCE OF GLOBAL WEAK SOLUTIONS TO SOME PROPERLY AND IMPROPERLY POSED PROBLEMS OF MATHEMATICAL PHYSICS - METHOD OF UNBOUNDED FOURIER COEFFICIENTS [J].

LEVINE, HA .

MATHEMATISCHE ANNALEN, 1975, 214 (03) :205-220

[8]

Li HX, 2014, ELECTRON J DIFFER EQ

[9] Blow-up phenomena for a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions [J].

Liu, Yan ;

Luo, Shiguang ;

Ye, Yunhua .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 65 (08) :1194-1199

[10] Bounds of the blowup time in parabolic equations with weighted source under nonhomogeneous Neumann boundary condition [J].

Lv, Xiaoshuang ;

Song, Xianfa .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (07) :1019-1028

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