Blow-up behavior outside the origin for a semilinear wave equation in the radial case - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bulletin des Sciences Mathématiques Année : 2011

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

Résumé

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 one-dimensional 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 $\{\frac 1R \le |x|\le R\}$ for any $R>1$.

Dates et versions

hal-00570157 , version 1 (27-02-2011)

Identifiants

Citer

Frank Merle, Hatem Zaag. Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Bulletin des Sciences Mathématiques, 2011, 135 (4), pp.353-373. ⟨10.1016/j.bulsci.2011.03.001⟩. ⟨hal-00570157⟩
98 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More