BLOW-UP OF SOLUTIONS TO SEMILINEAR WAVE EQUATIONS WITH SPATIAL DERIVATIVES

被引：2

作者：

Shao, Kerun ^{[1
]}

Takamura, Hiroyuki ^{[2
]}

Wang, Chengbo ^{[1
]}

机构：

[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310058, Peoples R China

[2] Tohoku Univ, Math Inst, Aoba Sendai 9808578, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2025年 / 45卷 / 02期

基金：

日本学术振兴会;

关键词：

Glassey conjecture; semilinear wave equation; blow-up; lifespan; critical exponents; GLOBAL EXISTENCE; BEHAVIOR;

D O I：

10.3934/dcds.2024098

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For small-amplitude semilinear wave equations with power type nonlinearity on the first-order spatial derivative, the expected sharp upper bound on the lifespan of solutions is obtained for both critical cases and subcritical cases, for all spatial dimensions n > 1. It is achieved uniformly by constructing the integral equations, deriving the ordinary differential inequality system, and iteration argument. Combined with the former works, the sharp lifespan estimates for this problem are completely established, at least for the spherical symmetric case.

引用

页码：410 / 424

页数：15

共 12 条

[1] Almost Global Existence for Some Semilinear Wave Equations with Almost Critical Regularity [J].

Fang, Daoyuan ;

Wang, Chengbo .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2013, 38 (09) :1467-1491

[2]

Glassey R.T., 1983, Comm. Partial Differential Equations

[3]

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

[4] 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

[5] Semilinear wave equations of derivative type with spatial weights in one space dimension [J].

Kitamura, Shunsuke ;

Morisawa, Katsuaki ;

Takamura, Hiroyuki .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2023, 72

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

RAMMAHA, MA .

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

[7] UPPER BOUNDS FOR THE LIFE-SPAN OF SOLUTIONS TO SYSTEMS OF NONLINEAR-WAVE EQUATIONS IN 2-SPACE AND 3-SPACE DIMENSIONS [J].

RAMMAHA, MA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 25 (06) :639-654

[8] The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative [J].

Sasaki, Takiko ;

Takamatsu, Shu ;

Takamura, Hiroyuki .

AIMS MATHEMATICS, 2023, 8 (11) :25477-25486

[9] 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

[10] 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

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