Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group
Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 01-14
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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 [10] and El Hamidi-Kirane [3] corresponding,
respectively, to the parabolic inequalities and parabolic system.
Keywords:
Fractional Derivatives, Heisenberg Group, Semilinear Differential Inequalities, 26A33, 33C60, 44A15, 35K55
@article{FCAA_2009_12_1_a0,
author = {Haouam, K. and Sfaxi, M.},
title = {Nonexistence {Results} of {Solutions} of {Semilinear} {Differential} {Inequalities} with {Temperal} {Fractional} {Derivative} on the {Heinsenberg} {Group}},
journal = {Fractional calculus and applied analysis},
pages = {01--14},
publisher = {mathdoc},
volume = {12},
number = {1},
year = {2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a0/}
}
TY - JOUR AU - Haouam, K. AU - Sfaxi, M. TI - Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group JO - Fractional calculus and applied analysis PY - 2009 SP - 01 EP - 14 VL - 12 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a0/ LA - en ID - FCAA_2009_12_1_a0 ER -
%0 Journal Article %A Haouam, K. %A Sfaxi, M. %T Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group %J Fractional calculus and applied analysis %D 2009 %P 01-14 %V 12 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a0/ %G en %F FCAA_2009_12_1_a0
Haouam, K.; Sfaxi, M. Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group. Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 01-14. http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a0/