2015 / December Volume 10 No.4
Structurally Stable Singularities for a Nonlinear Wave Equation
Published Date |
2015 / December
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Title | Structurally Stable Singularities for a Nonlinear Wave Equation |
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Pagination | 449-478 |
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.
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AMS Subject Classification |
35Q35, 35L70, 35L65.
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Received |
2015-07-10
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Accepted |
2015-06-02
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