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

Ahmed Alsaedi; Bashir Ahmad; Mokhtar Kirane; Aberrazak Nabti

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

Ahmed Alsaedi, Bashir Ahmad, Mokhtar Kirane, Aberrazak Nabti

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the higher order diffusion Schrödinger equation with a time nonlocal nonlinearity (formula presented) posed in (η, t) ∈ H×(0, +∞), supplemented with an initial data u(η, 0) = f(η), where m > 1, p > 1, < α < 1, and ∆_H is the Laplacian operator on the (2N + 1)-dimensional Heisenberg group 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.

Original language	British English
Pages (from-to)	1-10
Number of pages	10
Journal	Electronic Journal of Differential Equations
Volume	2020
State	Published - 2020

Keywords

Heisenberg group
Life span
Riemann-Liouville fractional integrals and derivatives
Schrödinger equation

Cite this

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title = "Lifespan of solutions of a fractional evolution equation with higher order diffusion on the heisenberg group",

abstract = "We consider the higher order diffusion Schr{\"o}dinger equation with a time nonlocal nonlinearity (formula presented) posed in (η, t) ∈ H×(0, +∞), supplemented with an initial data u(η, 0) = f(η), where m > 1, p > 1, < α < 1, and ∆H is the Laplacian operator on the (2N + 1)-dimensional Heisenberg group 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.",

keywords = "Heisenberg group, Life span, Riemann-Liouville fractional integrals and derivatives, Schr{\"o}dinger equation",

author = "Ahmed Alsaedi and Bashir Ahmad and Mokhtar Kirane and Aberrazak Nabti",

note = "Funding Information: Acknowledgements. This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, under grant no. (RG-36-130-40). The authors, therefore, acknowledge with thanks DSR technical and financial support. Publisher Copyright: {\textcopyright}2020 Texas State University.",

year = "2020",

language = "British English",

volume = "2020",

pages = "1--10",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

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TY - JOUR

T1 - Lifespan of solutions of a fractional evolution equation with higher order diffusion on the heisenberg group

AU - Alsaedi, Ahmed

AU - Ahmad, Bashir

AU - Kirane, Mokhtar

AU - Nabti, Aberrazak

N1 - Funding Information: Acknowledgements. This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, under grant no. (RG-36-130-40). The authors, therefore, acknowledge with thanks DSR technical and financial support. Publisher Copyright: ©2020 Texas State University.

PY - 2020

Y1 - 2020

N2 - We consider the higher order diffusion Schrödinger equation with a time nonlocal nonlinearity (formula presented) posed in (η, t) ∈ H×(0, +∞), supplemented with an initial data u(η, 0) = f(η), where m > 1, p > 1, < α < 1, and ∆H is the Laplacian operator on the (2N + 1)-dimensional Heisenberg group 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.

AB - We consider the higher order diffusion Schrödinger equation with a time nonlocal nonlinearity (formula presented) posed in (η, t) ∈ H×(0, +∞), supplemented with an initial data u(η, 0) = f(η), where m > 1, p > 1, < α < 1, and ∆H is the Laplacian operator on the (2N + 1)-dimensional Heisenberg group 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.

KW - Heisenberg group

KW - Life span

KW - Riemann-Liouville fractional integrals and derivatives

KW - Schrödinger equation

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M3 - Article

AN - SCOPUS:85078285402

SN - 1072-6691

VL - 2020

SP - 1

EP - 10

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

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

Abstract

Keywords

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