Electron. J. Differential Equations, Vol. 2020 (2020), No. 02, pp. 1-10.

Lifespan of solutions of a fractional evolution equation with higher order diffusion on the Heisenberg group

Ahmed Alsaedi, Bashir Ahmad, Mokhtar Kirane, Aberrazak Nabti

Abstract:
We consider the higher order diffusion Schrodinger equation with a time nonlocal nonlinearity

posed in $(\eta, t) \in \mathbb{H}\times(0,+\infty)$, supplemented with an initial data $u(\eta,0)=f(\eta)$, where $m>1,\,p>1,\,0<\alpha<1$, and $\Delta_{\mathbb{H}}$ is the Laplacian operator on the $(2N+1)$-dimensional Heisenberg group $\mathbb{H}$. Then, we prove a blow up result for its solutions. Furthermore, we give an upper bound estimate of the life span of blow up solutions.

Submitted June 8, 2019. Published January 7, 2020.
Math Subject Classifications: 35Q55, 35B44, 26A33, 35B30.
Key Words: Schrodinger equation; Heisenberg group; life span; Riemann-Liouville fractional integrals and derivatives.

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Ahmed Alsaedi
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group
Faculty of Sciences
King Abdulaziz University
Jeddah 21589, Saudi Arabia
email: aalsaedi@hotmail.com
Bashir Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group
Faculty of Sciences
King Abdulaziz University
Jeddah 21589, Saudi Arabia
email: bashirahmad\_qau@yahoo.com
Mokhtar Kirane
LASIE, Faculté des Sciences et Technologies
Université de La Rochelle
Avenue M. Crepeau, 17000
La Rochelle, France
email: mkirane@univ-lr.fr
Abderrazak Nabti
Laboratoire de Mathématiques
Informatiques et Systèmes (LAMIS)
Université Larbi Tebessi
12002 Tebessa, Algeria
email: abderrazaknabti@gmail.com

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