INTERACTIONS OF SEMILINEAR PROGRESSING WAVES IN TWO OR MORE SPACE DIMENSIONS

被引：12

作者：

Barreto, Antonio Sa ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, 150 North Univ St, W Lafayette, IN 47907 USA

来源：

INVERSE PROBLEMS AND IMAGING | 2020年 / 14卷 / 06期

基金：

美国国家科学基金会;

关键词：

Semilinear wave equations; propagation of singularities; wave front sets; initial value problems for wave equations; asymptotic behavior of solutions to wave equations; NONLINEAR-INTERACTION; SYMBOLIC-CALCULUS; SINGULARITIES; EQUATIONS; PROPAGATION; CONORMALITY;

D O I：

10.3934/ipi.2020055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the behavior of the singularities of solutions of semilinear wave equations after the interaction of three transversal conormal waves. Our results hold for space dimensions two and higher, and for arbitrary C-infinity nonlinearity. The case of two space dimensions in which the nonlinearity is a polynomial was studied by the author and Yiran Wang. We also indicate possible applications to inverse problems.

引用

页码：1057 / 1105

页数：49

共 50 条

[21] Stability of travelling waves in a model for conical flames in two space dimensions
Hamel, F
Monneau, R
Roquejoffre, JM
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2004, 37 (03): : 469 - 506
[22] The asymptotic theory of initial value problems for semilinear perturbed wave equations in two space dimensions
Lai, SY
Fu, QL
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2003, 24 (01) : 82 - 91
[23] 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
[24] The asymptotic theory of initial value problems for semilinear pertubed wave equations in two space dimensions
Lai Shao-yong
Fu Qing-long
Applied Mathematics and Mechanics, 2003, 24 (1) : 82 - 91
[25] The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions
Imai, Takuto
Kato, Masakazu
Takamura, Hiroyuki
Wakasa, Kyouhei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (10) : 8387 - 8424
[26] THE ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR SEMILINEAR PERTURBED WAVE EQUATIONS IN TWO SPACE DIMENSIONS
赖绍永
胡青龙
AppliedMathematicsandMechanics(EnglishEdition), 2003, (01) : 82 - 91
[27] The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions
Imai, Takuto
Kato, Masakazu
Takamura, Hiroyuki
Wakasa, Kyouhei
ASYMPTOTIC ANALYSIS FOR NONLINEAR DISPERSIVE AND WAVE EQUATIONS, 2019, 81 : 31 - 53
[28] Remarks on weaker null conditions for two kinds of systems of semilinear wave equations in three space dimensions
Cheng, Minggang
Katayama, Soichiro
HOKKAIDO MATHEMATICAL JOURNAL, 2024, 53 (01) : 139 - 174
[29] Lower bounds of the life span of classical solutions to a system of semilinear wave equations in two space dimensions
Di Flaviano, M
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 281 (01) : 22 - 45
[30] BLOW UP FOR INITIAL BOUNDARY VALUE PROBLEM OF CRITICAL SEMILINEAR WAVE EQUATION IN TWO SPACE DIMENSIONS
Lai, Ning-An
Zhou, Yi
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (04) : 1499 - 1510

← 1 2 3 4 5 →