On certain time- and space-fractional evolution systems

Ahmad Fino (1, 2) , Mokhtar Kirane (1)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 LaMA--Liban - Laboratoire de mathématiques et applications

In this paper, we investigate the local existence and the finite-time blow-up of solutions of semilinear parabolic system with nonlocal in time nonlinearity. In addition, we also give the blow-up rate and necessary conditions for local and global existence.

Mots clés: Riemann-Liouville fractional integrals and derivatives; Parabolic system; local existence; mild and weak solution; blow-up; blow-up rate; maximal regularity; interior regularity; schauder's estimates; Riemann-Liouville fractional integrals and derivatives.

Domaines: Equations aux dérivées partielles [math.AP]

Ahmad Fino, Mokhtar Kirane. On certain time- and space-fractional evolution systems. 2009. ⟨hal-00414092⟩