Remarks on weaker null conditions for two kinds of systems of semilinear wave equations in three space dimensions

被引：0

作者：

Cheng, Minggang ^{[1
]}

Katayama, Soichiro ^{[1
]}

机构：

[1] Osaka Univ, Dept Math, Grad Sch Sci, 1-1 Machikaneyama, Toyonaka, Osaka 5600043, Japan

来源：

HOKKAIDO MATHEMATICAL JOURNAL | 2024年 / 53卷 / 01期

关键词：

Semilinear wave equation; Klein-Gordon equation; multiple propagation speeds; null condition; weak null condition; global existence; KLEIN-GORDON EQUATIONS; GLOBAL EXISTENCE; NONLINEAR-WAVE; HYPERBOLIC SYSTEMS; ENERGY DECAY;

D O I：

10.14492/hokmj/2022-637

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Cauchy problems for systems of nonlinear wave and Klein -Gordon equations, or for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Global existence of solutions under the so-called null condition is already known for these systems. Our aim here is to obtain the global existence for these systems with some kinds of nonlinearities violating the null condition.

引用

页码：139 / 174

页数：36

共 50 条

[1] SYSTEMS OF SEMILINEAR WAVE EQUATIONS WITH MULTIPLE SPEEDS IN TWO SPACE DIMENSIONS AND A WEAKER NULL CONDITION
Cheng, Minggang
Katayama, Soichiro
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2022, 21 (09) : 3117 - 3139
[2] ASYMPTOTIC POINTWISE BEHAVIOR FOR SYSTEMS OF SEMILINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS
Katayama, Soichiro
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2012, 9 (02) : 263 - 323
[3] The asymptotic theory for semilinear wave equations in two space dimensions
Tan, XK
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS AND COMPUTATIONAL SIMULATIONS, 2000, : 311 - 315
[4] Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
Katayama, Soichiro
Matsumura, Akitaka
Sunagawa, Hideaki
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (04): : 601 - 628
[5] Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
Soichiro Katayama
Akitaka Matsumura
Hideaki Sunagawa
Nonlinear Differential Equations and Applications NoDEA, 2015, 22 : 601 - 628
[6] Generalized wave operators for a system of semilinear wave equations in three space dimensions
Kubo, Hideo
Kubota, Koji
HOKKAIDO MATHEMATICAL JOURNAL, 2013, 42 (01) : 81 - 111
[7] Initial value problem of semilinear wave equations in three space dimensions
Hidano, K
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 26 (05) : 941 - 970
[8] Initial value problem of semilinear wave equations in three space dimensions
Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku, Tokyo 169, Japan
Nonlinear Anal Theory Methods Appl, 5 (941-970):
[9] Scattering for the quasilinear wave equations with null conditions in two dimensions
He, Daoyin
Liu, Jie
Wang, Keyan
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (04) : 3067 - 3088
[10] Critical blowup for systems of semilinear wave equations in low space dimensions
Kubo, H
Ohta, M
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 240 (02) : 340 - 360

← 1 2 3 4 5 →