Blow-up problems for a parabolic equation coupled with superlinear source and local linear boundary dissipation

被引：3

作者：

Sun, Fenglong ^{[1
]}

Wang, Yutai ^{[1
]}

Yin, Hongjian ^{[1
]}

机构：

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 514卷 / 02期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Parabolic equation; Boundary dissipation; Finite time blow-up; Concavity method; Blow up time; HEAT-EQUATION; WAVE-EQUATION; NONEXISTENCE THEOREMS; WELL-POSEDNESS;

D O I：

10.1016/j.jmaa.2022.126327

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the finite time blow-up results for a parabolic equation coupled with superlinear source term and local linear boundary dissipation. Using a concavity argument, we derive the sufficient conditions for the solutions to blow up in finite time. In particular, we obtain the existence of finite time blow-up solutions with arbitrary high initial energy. We also derive the upper bound and lower bound of the blow up time. (C) 2022 Elsevier Inc. All rights reserved.

引用

页数：17

共 18 条

[1]

Bejenaru I, 2001, ELECTRON J DIFFER EQ

[2] Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction [J].

Cavalcanti, Marcelo M. ;

Cavalcanti, Valeria N. Domingos ;

Lasiecka, Irena .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 236 (02) :407-459

[3] On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation [J].

Chueshov, I ;

Eller, M ;

Lasiecka, I .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2002, 27 (9-10) :1901-1951

[4]

Ciarlet P.G., 2013, Linear and Nonlinear Functional Analysis with Applications

[5] Transversality of stable and Nehari manifolds for a semilinear heat equation [J].

Dickstein, Flavio ;

Mizoguchi, Noriko ;

Souplet, Philippe ;

Weissler, Fred .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2011, 42 (3-4) :547-562

[6] LOCAL HADAMARD WELL-POSEDNESS AND BLOW UP FOR REACTION DIFFUSION EQUATIONS WITH NON LINEAR DYNAMICAL BOUNDARY CONDITIONS [J].

Fiscella, Alessio ;

Vitillaro, Enzo .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (11-12) :5015-5047

[7] EVOLUTION-EQUATIONS WITH DYNAMIC BOUNDARY-CONDITIONS [J].

HINTERMANN, T .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1989, 113 :43-60

[8] NONEXISTENCE THEOREMS FOR HEAT EQUATION WITH NONLINEAR BOUNDARY-CONDITIONS AND FOR POROUS-MEDIUM EQUATION BACKWARD IN TIME [J].

LEVINE, HA ;

PAYNE, LE .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1974, 16 (02) :319-334

[9]

LEVINE HA, 1973, ARCH RATION MECH AN, V51, P371

[10] A POTENTIAL WELL THEORY FOR THE HEAT-EQUATION WITH A NONLINEAR BOUNDARY-CONDITION [J].

LEVINE, HA ;

SMITH, RA .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1987, 9 (02) :127-136

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