The lifespan of solutions to wave equations with weighted nonlinear terms in one space dimension

被引：9

作者：

Wakasa, Kyouhei ^{[1
]}

机构：

[1] Muroran Inst Technol, Math Sci Res Unit, Coll Liberal Arts, 27-1 Mizumoto Cho, Muroran, Hokkaido 0508585, Japan

来源：

HOKKAIDO MATHEMATICAL JOURNAL | 2017年 / 46卷 / 02期

关键词：

nonlinear wave equation; lifespan; one space dimension; BLOW-UP;

D O I：

10.14492/hokmj/1498788020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the initial value problem for nonlinear wave equation with weighted nonlinear terms in one space dimension. Kubo & Osaka & Yazici [4] studied global solvability of the problem under different conditions on the nonlinearity and initial data, together with an upper bound of the lifespan for the problem. The aim of this paper is to improve the upper bound of the lifespan and to derive its lower bound which shows the optimality of our new upper bound.

引用

页码：257 / 276

页数：20

共 7 条

[1] Critical curve for p-q systems of nonlinear wave equations in three space dimensions
Agemi, R
Kurokawa, Y
Takamura, H
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 167 (01) : 87 - 133
[2] BLOW-UP OF SOLUTIONS OF NON-LINEAR WAVE-EQUATIONS IN 3 SPACE DIMENSIONS
JOHN, F
[J]. MANUSCRIPTA MATHEMATICA, 1979, 28 (1-3) : 235 - 268
[3] BLOW-UP OF SOLUTIONS OF SOME NON-LINEAR HYPERBOLIC-EQUATIONS
KATO, T
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (04) : 501 - 505
[4] Kubo H., 2013, INTERDISCIP INF SCI, V19, P143, DOI DOI 10.4036/iis.2013.143
[5] Suzuki A, 2010, THESIS
[6] Almost global solutions of semilinear wave equations with the critical exponent in high dimensions
Takamura, Hiroyuki
Wakasa, Kyouhei
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 109 : 187 - 229
[7] ZHOU Y, 1992, CHINESE ANN MATH B, V13, P230

← 1 →