Structurally Stable Singularities for a Nonlinear Wave Equation

Abstract

For the nonlinear wave equation $u_{tt}-c(u)(c(u)u_x{)}_x=0$, it is well known that solutions can develop singularities in finite time. For an open dense set of initial data, the present paper provides a detailed asymptotic description of the solution in a neighborhood of each singular point, where $|u_x|\to \infty$. The different structure of conservative and dissipative solutions is analyzed.

References in corpus (2)

• Global Conservative Solutions to a Nonlinear Variational Wave Equation
• Unique Conservative Solutions to a Variational Wave Equation

Cited by in corpus (4)

• Uniqueness of conservative solutions to a one-dimensional general quasilinear wave equation through variational principle
• Lipschitz Metrics for a Class of Nonlinear Wave Equations
• A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation
• Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation