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arXiv · 1503.08807

Structurally Stable Singularities for a Nonlinear Wave Equation

Alberto Bressan·Tao Huang·Fang Yu
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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.

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Alberto Bressan, Tao Huang, Fang Yu. 2015-03-30. Structurally Stable Singularities for a Nonlinear Wave Equation. https://arxiv.org/abs/1503.08807

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