English

Structurally Stable Singularities for a Nonlinear Wave Equation

Analysis of PDEs 2015-03-31 v1

Abstract

For the nonlinear wave equation uttc(u)(c(u)ux)x = 0u_{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 ux|u_x|\to\infty. The different structure of conservative and dissipative solutions is analyzed.

Keywords

Cite

@article{arxiv.1503.08807,
  title  = {Structurally Stable Singularities for a Nonlinear Wave Equation},
  author = {Alberto Bressan and Tao Huang and Fang Yu},
  journal= {arXiv preprint arXiv:1503.08807},
  year   = {2015}
}
R2 v1 2026-06-22T09:06:05.238Z