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Structurally Stable Singularities for a Nonlinear Wave Equation
by Alberto Bressan   Tao Huang   Fang Yu

Vol. 10 No. 4 (2015) P.449~P.478

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 infinite 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 $\left |u_{x} \right |$ $\rightarrow$ $\infty$. The different structure of conservative and dissipative solutions is analyzed.

KEYWORDS
Nonlinear wave equation, singularities, asymptotic structure.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35Q35, 35L70, 35L65.

MILESTONES

Revised : 2015-07-10
Accepted: 2015-06-02