Focusing of spherical nonlinear pulses in R1+3 and scattering

被引：4

作者：

Carles, R

Rauch, J

机构：

[1] Univ Rennes 1, ENS Cachan, F-35170 Bruz, France

[2] Univ Rennes 1, IRMAR, F-35170 Bruz, France

[3] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 2001年 / 332卷 / 12期

关键词：

D O I：

10.1016/S0764-4442(01)01971-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the validity of geometric optics for nonlinear wave equations in three space dimensions whose solutions, pulse like, focus at a point. If the amplitude of the initial data is critical, linear geometric optics is valid before the focal point, as well as after The matching between these two regimes is described by a scattering operator which enlarges the support of the waves. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

引用

页码：1077 / 1082

页数：6