GLOBAL EXISTENCE FOR SEMILINEAR DAMPED WAVE EQUATIONS IN THE SCATTERING CASE

被引：0

作者：

Bai, Yige ^{[1
]}

Liu, Mengyun ^{[1
]}

机构：

[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2019年 / 32卷 / 3-4期

关键词：

TIME-DEPENDENT DISSIPATION; BLOW-UP; GLASSEY CONJECTURE; BEHAVIOR;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the global existence of solutions to semilinear damped wave equations in the scattering case with power-type non linearity on the derivatives, posed on nontrapping asymptotically Euclidean manifolds. The main idea is to shift initial time by local existence. As a result, we could convert the damping term to small enough perturbation and obtain the global existence.

引用

页码：233 / 248

页数：16

共 18 条

[1]

An Lai N., DIFFERENTIAL INTEGRA

[2]

Glassey R. T., 1983, COMM PARTIAL DIFFERE

[3]

Hidano K, 1995, INDIANA U MATH J, V44, P1273

[4] Combined effects of two nonlinearities in lifespan of small solutions to semi-linear wave equations [J].

Hidano, Kunio ;

Wang, Chengbo ;

Yokoyama, Kazuyoshi .

MATHEMATISCHE ANNALEN, 2016, 366 (1-2) :667-694

[5] The Glassey conjecture with radially symmetric data [J].

Hidano, Kunio ;

Wang, Chengbo ;

Yokoyama, Kazuyoshi .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2012, 98 (05) :518-541

[6] Global parametrices and dispersive estimates for variable coefficient wave equations [J].

Metcalfe, Jason ;

Tataru, Daniel .

MATHEMATISCHE ANNALEN, 2012, 353 (04) :1183-1237

[7] FINITE-TIME BLOW-UP FOR NONLINEAR-WAVE EQUATIONS IN HIGH DIMENSIONS [J].

RAMMAHA, MA .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1987, 12 (06) :677-700

[8] FINITE-TIME BLOW-UP FOR UTT-DELTA-U=H(UR,UT) IN 2 SPACE DIMENSIONS [J].

SCHAEFFER, J .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1986, 11 (05) :513-543

[9] GLOBAL BEHAVIOR OF SOLUTIONS TO NON-LINEAR WAVE-EQUATIONS IN 3 DIMENSIONS [J].

SIDERIS, TC .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1983, 8 (12) :1291-1323

[10] Global Strichartz estimates for nontrapping perturbations of the Laplacian. [J].

Smith, HF ;

Sogge, CD .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2000, 25 (11-12) :2171-2183

← 1 2 →