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

Fractional Calculus and Applied Analysis (2009)

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

## Access Full Article

top## Abstract

top## How to cite

topHaouam, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.