INTERACTIONS OF SEMILINEAR PROGRESSING WAVES IN TWO OR MORE SPACE DIMENSIONS

被引：14

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 44 条

[11]

Bony J.-M., 1978, JOURN E D P ST JEAN

[12]

Bony J.-M., 1984, P INT C MATH, V1, P1133

[13]

Bony J.-M., 1981, SEM GOULAOUIC MEYER, V2

[14]

Bony J-M., 1984, GOULAOUIC MEYER SCHW

[15]

BONY JM, 1981, ANN SCI ECOLE NORM S, V14, P209

[16] INTERACTION OF THE 3 WAVES IN STRICTLY HYPERBOLIC SEMILINEAR EQUATIONS OF THE 2ND-ORDER [J].

CHEMIN, JY .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1987, 12 (11) :1203-1225

[17]

Chen X., ARXIV190205711

[18] CONORMALITY OF SEMILINEAR WAVES ALONG THE CAUSTICS [J].

DELORT, JM .

AMERICAN JOURNAL OF MATHEMATICS, 1991, 113 (04) :593-651

[19]

Duistermaat J. J., 1996, SERIES PROGR MATH, V130

[20]

Fiorenza A., ARXIV181204281

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