Qualitative Properties of Solutions to a Time-Space Fractional Evolution Equation

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 analyze a spatio-temporally nonlocal nonlinear parabolic equation. First, we valid the equation by an existence-uniqueness result. Then, we show that blowing-up solutions exist and study their time blow-up profile. Also, a result on the existence of global solutions is presented. Furthermore, we establish necessary conditions for local or global existence.

Keywords: Parabolic equation; fractional Laplacian; Riemann-Liouville fractional integrals and derivatives; local existence; critical exponent; blow-up rate

Domains: Analysis of PDEs [math.AP]

Ahmad Fino, Mokhtar Kirane. Qualitative Properties of Solutions to a Time-Space Fractional Evolution Equation. 2009. ⟨hal-00398110v5⟩