Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

Haouam, K., and Sfaxi, M.. "Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group." Fractional Calculus and Applied Analysis 12.1 (2009): 01-14. <http://eudml.org/doc/11312>.

@article{Haouam2009,
abstract = {2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55Denoting 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.},
author = {Haouam, K., Sfaxi, M.},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 33C60; 44A15; 35K55},
language = {eng},
number = {1},
pages = {01-14},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group},
url = {http://eudml.org/doc/11312},
volume = {12},
year = {2009},
}

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
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 12
IS - 1
SP - 01
EP - 14
AB - 2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55Denoting 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.
LA - eng
KW - 26A33; 33C60; 44A15; 35K55
UR - http://eudml.org/doc/11312
ER -