A Liouville theorem for the Degasperis-Procesi equation

Lorenzo Brandolese (1)

1 EDPA - Équations aux dérivées partielles, analyse

We prove that the only global, strong, spatially periodic solution to the Degasperis-Procesi equation, vanishing at some point (t0, x0), is the identically zero solution. We also establish the analogue of such Liouville-type theorem for the Degasperis-Procesi equation with an additional dispersive term.

Mots clés: Integrable systems; Nonlinear dispersive waves; Wave breaking; Shallow water; Blowup

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brandolese. A Liouville theorem for the Degasperis-Procesi equation. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2016, XVI (3), pp.759-765. ⟨hal-00996383v2⟩