Finite time blow-up for a wave equation with a nonlocal nonlinearity

Ahmad Fino (1, 2, 3) , Mokhtar Kirane (3) , Vladimir Georgiev (4)

1 LaMA--Liban - Laboratoire de mathématiques et applications
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
3 MIA - Mathématiques, Image et Applications - EA 3165
4 Dipartimento di Matematica [Pisa]

In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear forcing term.

Mots clés: Hyperbolic equation; mild and weak solutions; local existence; Strichartz estimate; blow-up; Riemann-Liouville fractional integrals and derivatives

Domaines: Equations aux dérivées partielles [math.AP]

Ahmad Fino, Mokhtar Kirane, Vladimir Georgiev. Finite time blow-up for a wave equation with a nonlocal nonlinearity. 2009. ⟨hal-00511349⟩