A nonexistence result for a nonlinear wave equation with damping on a Riemannian manifold

被引：3

作者：

Ru, Qiang ^{[1
]}

机构：

[1] China Univ Min & Technol, Dept Math, Xuzhou 221116, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2016年

基金：

中国国家自然科学基金;

关键词：

nonexistence; wave equation; CRITICAL EXPONENT; THEOREMS;

D O I：

10.1186/s13661-016-0705-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the global nonexistence of solutions to a nonlinear wave equation with critical potential V(x) on a Riemannian manifold, the form of which is more general than those in (Todorova and Yordanov in C.R. Acad. Sci., Ser. 1 Math. 300: 557-562, 2000). The way we follow is motivated by the work of Qi S. Zhang (C.R. Acad. Sci., Ser. 1 Math. 333: 109-114, 2001). We also prove the local existence and uniqueness result.

引用

页数：10

共 13 条

[1]

DETURCK DM, 1981, ANN SCI ECOLE NORM S, V14, P249

[2] Hyperbolic mean curvature flow [J].

He, Chun-Lei ;

Kong, De-Xing ;

Liu, Kefeng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (01) :373-390

[3]

Hormander Lars, 1997, Mathematiques & Applications (Berlin) Mathematics & Applications, V26

[4]

Kong D-X, 2007, J MATH PHYS, V48, P1

[5] THE ROLE OF CRITICAL EXPONENTS IN BLOWUP THEOREMS [J].

LEVINE, HA .

SIAM REVIEW, 1990, 32 (02) :262-288

[6] Critical exponent for semilinear wave equation with critical potential [J].

Li, Xinfu .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2013, 20 (03) :1379-1391

[7] CRITICAL EXPONENT FOR THE SEMILINEAR WAVE EQUATION WITH TIME-DEPENDENT DAMPING [J].

Lin, Jiayun ;

Nishihara, Kenji ;

Zhai, Jian .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (12) :4307-4320

[8] Critical exponent for a nonlinear wave equation with damping [J].

Todorova, G ;

Yordanov, B .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (07) :557-562

[9]

Wakasugi Y, 2014, TRENDS MATH, P375

[10] A new critical phenomenon for semilinear parabolic problems [J].

Zhang, QS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 219 (01) :125-139

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