On certain time-space fractional evolution equations
Résumé
In this article, we present first a new technique to prove, in a general case, the recent result of Cazenave, Dickstein and Weissler on the blowing-up solutions to a temporally nonlocal nonlinear parabolic equation. Then, we study the blow-up rate, and the existence of global solutions. Furthermore, we establish necessary conditions for local or global existence.
Mots clés
Parabolic equation
mild and weak solutions
Riemann-Liouville fractional integrals and derivatives
local and global existence
blow-up
blow-up rate
maximal regularity
interior regularity
Schauder's estimates
critical exponent
fractional Laplacian
Riemann-Liouville fractional integrals and derivatives.
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