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# 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 $|u_x| → ∞$. The different structure of conservative and dissipative solutions is analyzed.

Paper:
Available as PDF (345 Kbytes).
Author(s):
Alberto Bressan,
Tao Huang,
Fang Yu,
Submitted by:
; 2015-04-03.