On certain time- and space-fractional evolution equations

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 article, we present first a new technique to prove, in a general case, the recent result of Cazenave, Dickstein and Weissler \cite{CDW} on the blowing-up solutions to a temporally nonlocal nonlinear parabolic equation.\\ Then, we study the blow-up rate and the global existence in time of the solutions. Furthermore, we show necessary conditions for global existence.\\

Mots clés: Parabolic equation; local and global existence; blow-up; blow-up rate; critical exponent; fractional laplacian; Riemann-Liouville fractional integrals and derivatives; Riemann-Liouville fractional integrals and derivatives.

Domaines: Equations aux dérivées partielles [math.AP]

Ahmad Fino, Mokhtar Kirane. On certain time- and space-fractional evolution equations. 2009. ⟨hal-00398110v2⟩