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Séminaire Équations aux dérivées partielles (Polytechnique)

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Jean-Luc Joly; Guy Métivier; Jeffrey Rauch
Nonlinear Hyperbolic Smoothing at a Focal Point
Séminaire Équations aux dérivées partielles (Polytechnique) (1998-1999), Exp. No. 5, 11 p.
Article PDF | Analyses MR 1721323 | Zbl 1059.35516

Résumé - Abstract

The nonlinear dissipative wave equation $u_{tt}-\Delta u + |u_t|^{h-1}u_t=0$ in dimension $d>1$ has strong solutions with the following structure. In $0\le t <1$ the solutions have a focusing wave of singularity on the incoming light cone $|x|=1-t$. In $\lbrace t\ge 1\rbrace $ that is after the focusing time, they are smoother than they were in $\lbrace 0\le t<1\rbrace $. The examples are radial and piecewise smooth in $\lbrace 0\le t<1 \rbrace $

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