Inverse problems for quadratic derivative nonlinear wave equations

被引：47

作者：

Wang, Yiran ^{[1
]}

Zhou, Ting ^{[2
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[2] Northeastern Univ, Dept Math, 360 Huntington Ave, Boston, MA 02115 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 44卷 / 11期

基金：

美国国家科学基金会;

关键词：

Inverse problems; Lorentzian metric; nonlinear wave equations; nonlinear interaction of singularities; quadratic derivatives nonlinearity; PROGRESSING WAVES; NULL FORMS; SINGULARITIES;

D O I：

10.1080/03605302.2019.1612908

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For semilinear wave equations on Lorentzian manifolds with quadratic derivative nonlinear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from the source-to-solution map, one can determine the Lorentzian metric up to diffeomorphisms.

引用

页码：1140 / 1158

页数：19

共 23 条

[1]

Bar C., 2007, ESI LECT MATH PHYS, DOI DOI 10.4171/037

[2]

Beals Michael., 1989, Progress in Nonlinear Differential Equations and Their Applications, V3

[3] On smooth Cauchy hypersurfaces and Geroch's splitting theorem [J].