Preprint 2015-011
Structurally stable singularities for a nonlinear wave equation
Alberto Bressan, Tao Huang and Fang Yu
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 $|u_x| → ∞$. The different structure of conservative and dissipative solutions is analyzed.