Nonlinear Hyperbolic Smoothing at a Focal Point
Séminaire Équations aux dérivées partielles (Polytechnique) (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}

@article{SEDP_1998-1999____A5_0,
     author = {Joly, Jean-Luc and M\'etivier, Guy and Rauch, Jeffrey},
     title = {Nonlinear Hyperbolic Smoothing at a Focal Point},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1998-1999},
     note = {talk:5},
     mrnumber = {1721323},
     zbl = {1059.35516},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_1998-1999____A5_0}
}
Joly, Jean-Luc; Métivier, Guy; Rauch, Jeffrey. Nonlinear Hyperbolic Smoothing at a Focal Point. Séminaire Équations aux dérivées partielles (Polytechnique) (1998-1999), Talk no. 5, 11 p. http://www.numdam.org/item/SEDP_1998-1999____A5_0/

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