Generic regularity of conservative solutions to a nonlinear wave equation

Alberto Bressan, Geng Chen

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

The paper is concerned with conservative solutions to the nonlinear wave equation utt−c(u)(c(u)ux)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 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.

Original languageEnglish (US)
Pages (from-to)335-354
Number of pages20
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume34
Issue number2
DOIs
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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