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Blow-up behavior outside the origin for a semilinear wave equation in the radial case

✍ Scribed by Frank Merle; Hatem Zaag

Publisher: Elsevier Science
Year: 2011
Tongue: French
Weight: 190 KB
Volume: 135
Category: Article
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2011.03.001

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✦ Synopsis

We consider the semilinear wave equation in the radial case with conformal subcritical power nonlinearity. If we consider a blow-up point different from the origin, then we exhibit a new Lyapunov functional which is a perturbation of the one-dimensional case and extend all our previous results known in the onedimensional case. In particular, we show that the blow-up set near non-zero non-characteristic points is of class C 1 , and that the set of characteristic points is made of concentric spheres in finite number in { 1 R |x| R} for any R > 1.

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