Generic regularity of conservative solutions to a nonlinear wave equation

Alberto Bressan; Geng Chen

doi:10.1016/j.anihpc.2015.12.004

Generic regularity of conservative solutions to a nonlinear wave equation

Alberto Bressan
, Geng Chen

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

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 C³ initial data, we prove that the solution is piecewise smooth in the t–x plane, while the gradient u_x 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.

Original language	English (US)
Pages (from-to)	335-354
Number of pages	20
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	34
Issue number	2
DOIs	https://doi.org/10.1016/j.anihpc.2015.12.004
State	Published - 2017

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2015.12.004

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Generic regularity of conservative solutions to a nonlinear wave equation

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