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

Haouam, K.; Sfaxi, M.

Fractional Calculus and Applied Analysis (2009)

  • Volume: 12, Issue: 1, page 01-14
  • ISSN: 1311-0454

Abstract

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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.

How to cite

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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 -

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