Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 12, No 1, (2009), 01p-14p
Denoting by Dα0|t the time-fractional derivative of order α (α ∈ (0, 1)) in the sense of Caputo, and by ∆H the Laplacian operator on the (2N + 1) - dimensional Heisenberg group H^N, we prove some nonexistence results for solutions to problems of the type
Dα0|tu − ∆H(au) >= |u|^p,
Dα0|tu − ∆H(au) >= |v|^p,
Dδ0|tv − ∆H(bv) >= |u|^q,
in H^N × R+ , with a, b ∈ L ∞ (H^N × R+).
For α = 1 (and δ = 1 in the case of two inequalities), we retrieve the
results obtained by Pohozaev-Véron  and El Hamidi-Kirane  corresponding,
respectively, to the parabolic inequalities and parabolic system.