Global existence and blow-up of solution for the semilinear wave equation with interior and boundary source terms

被引：5

作者：

Zhang, Hongwei ^{[1
]}

Zhang, Wenxiu ^{[1
]}

Hu, Qingying ^{[1
]}

机构：

[1] Henan Univ Technol, Dept Math, Zhengzhou, Henan, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2019年 / 2019卷 / 1期

基金：

中国国家自然科学基金;

关键词：

Global existence; Blow-up; Dynamical boundary condition; Wave equation; Potential well theory; NONLINEAR BOUNDARY; WEAK SOLUTIONS; DECAY; UNIQUENESS; CRITERION; SYSTEMS; ENERGY;

D O I：

10.1186/s13661-019-1129-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with semilinear wave equations with nonlinear interior and boundary sources and subject to a nonlinear dynamical boundary condition. By using the potential well method combined with a standard continuous argument, under appropriate assumptions imposed on the source term, we establish global existence of solutions. Moreover, for certain initial data in the unstable set, the finite time blow-up phenomenon is exhibited.

引用

页数：10

共 30 条

[1] On the Blow-Up Criterion for Incompressible Stokes-MHD Equations [J].

Alghamdi, Ahmad Mohammad ;

Gala, Sadek ;

Ragusa, Maria Alessandra .

RESULTS IN MATHEMATICS, 2018, 73 (03)

[2]

ALSHIN AB, 1998, DOKL MATH, V58, P148

[3]

Bociu L., 2008, Appl. Math., V35, P281, DOI [DOI 10.4064/AM35-3-3, 10.4064/am35-3-3]

[4]

Bociu L, 2008, DISCRETE CONT DYN-A, V22, P835

[5] Wave equations with super-critical interior and boundary nonlinearities [J].

Bociu, Lorena ;

Rammaha, Mohammad ;

Toundykov, Daniel .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2012, 82 (06) :1017-1029

[6] On a wave equation with supercritical interior and boundary sources and damping terms [J].

Bociu, Lorena ;

Rammaha, Mohammad ;

Toundykov, Daniel .

MATHEMATISCHE NACHRICHTEN, 2011, 284 (16) :2032-2064

[7] Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping [J].

Bociu, Lorena ;

Lasiecka, Irena .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (03) :654-683

[8] Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping [J].

Bociu, Lorena .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) :E560-E575

[9]

Cavalcanti M. M., 2006, ADV MATH SCI APPL, V16, P661

[10] 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

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