Liouville Type Theorems for Fractional Parabolic Problems.

The purpose of this paper is twofold. Firstly, we establish optimal Liouville type theorems for nonnegative or positive supersolutions of the fractional parabolic equation u t + (- Δ) s u = u p on the whole space R N × R , where p ∈ R and 0 < s < 1 . Secondly, we study similar questions for the fractional parabolic system u t + (- Δ) s u = v p v t + (- Δ) s v = u q , where p and q are real numbers. [ABSTRACT FROM AUTHOR]