Generic regularity of conservative solutions to a nonlinear wave equation

被引：35

作者：

Bressan, Alberto ^{[1
]}

Chen, Geng ^{[2
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2017年 / 34卷 / 02期

基金：

美国国家科学基金会;

关键词：

Nonlinear wave equations; Generic regularity; Singularity; PARTIAL-DIFFERENTIAL-EQUATIONS; SINGULARITIES;

D O I：

10.1016/j.anihpc.2015.12.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper is concerned with conservative solutions to the nonlinear wave equation u(tt) -c(u)(c(u)u(x))(x) = 0. For an open dense set of C-3 initial data, we prove that the solution is piecewise smooth in the t-x plane, while the gradient ux can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem. (C) 2015 Elsevier Masson SAS. All rights reserved.

引用

页码：335 / 354

页数：20

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