Structurally Stable Singularities for a Nonlinear Wave Equation

2015/03/30 by Alberto Bressan, Bressan, Alberto, Tao Huang +4 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1503.08807

arxiv created 2015/03/30 · openalex publication_date 2015/03/30 · arxiv updated 2015/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation
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