Nonlinear Hyperbolic Smoothing at a Focal Point
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Talk no. 5, 11 p.

The nonlinear dissipative wave equation u tt -Δu+|u t | h-1 u t =0 in dimension d>1 has strong solutions with the following structure. In 0t<1 the solutions have a focusing wave of singularity on the incoming light cone |x|=1-t. In {t1} that is after the focusing time, they are smoother than they were in {0t<1}. The examples are radial and piecewise smooth in {0t<1}

Joly, Jean-Luc 1; Métivier, Guy 2; Rauch, Jeffrey 3

1 MAB, Université de Bordeaux I, 33405 Talence, FRANCE
2 IRMAR, Université de Rennes I,35042 Rennes, FRANCE
3 Department of Mathematics, University of Michigan, Ann Arbor 48109 MI, USA
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     title = {Nonlinear {Hyperbolic} {Smoothing} at a {Focal} {Point}},
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Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey. Nonlinear Hyperbolic Smoothing at a Focal Point. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Talk no. 5, 11 p. http://www.numdam.org/item/SEDP_1998-1999____A5_0/

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