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 , which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem.
|Original language||English (US)|
|Number of pages||20|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - 2017|
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Applied Mathematics