Year: 2015
Type: preprint
Abstract: For the nonlinear wave equation $u_{tt} - c(u)\big(c(u) u_x\big)_x~=~0$, 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.
Source: arXiv (Cornell University)
Authors: Bressan, Alberto, Huang, Tao, Yu, Fang
Institution: Pennsylvania State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2466384229