Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations

Bashir Ahmad; Ahmed Alsaedi; Mohamed Berbiche; Mokhtar Kirane

Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations

Bashir Ahmad
, Ahmed Alsaedi
, Mohamed Berbiche
, Mokhtar Kirane

Mathematics

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

5 Scopus citations

Abstract

We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in R₊×R^N. Under appropriate conditions on the exponents and the orders of the fractional time derivatives, we present a critical value of the dimension N, for which global solutions with small data exist, otherwise solutions blow-up in finite time. Furthermore, the large time behavior of global solutions is discussed.

Original language	British English
Article number	110
Pages (from-to)	1-28
Number of pages	28
Journal	Electronic Journal of Differential Equations
Volume	2020
State	Published - 2020

Keywords

Blow-up
Coupled fractional-diffusion equations
Global solution
Polynomial nonlinearities

Cite this

@article{ad1cfb0d3f8549c2ada77f2457afead9,

title = "Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations",

abstract = "We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in R+×RN. Under appropriate conditions on the exponents and the orders of the fractional time derivatives, we present a critical value of the dimension N, for which global solutions with small data exist, otherwise solutions blow-up in finite time. Furthermore, the large time behavior of global solutions is discussed.",

keywords = "Blow-up, Coupled fractional-diffusion equations, Global solution, Polynomial nonlinearities",

author = "Bashir Ahmad and Ahmed Alsaedi and Mohamed Berbiche and Mokhtar Kirane",

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-39-130-38. 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--28",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

}

TY - JOUR

T1 - Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations

AU - Ahmad, Bashir

AU - Alsaedi, Ahmed

AU - Berbiche, Mohamed

AU - Kirane, Mokhtar

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-39-130-38. The authors, therefore, acknowledge with thanks DSR technical and financial support. Publisher Copyright: © 2020 Texas State University.

PY - 2020

Y1 - 2020

N2 - We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in R+×RN. Under appropriate conditions on the exponents and the orders of the fractional time derivatives, we present a critical value of the dimension N, for which global solutions with small data exist, otherwise solutions blow-up in finite time. Furthermore, the large time behavior of global solutions is discussed.

AB - We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in R+×RN. Under appropriate conditions on the exponents and the orders of the fractional time derivatives, we present a critical value of the dimension N, for which global solutions with small data exist, otherwise solutions blow-up in finite time. Furthermore, the large time behavior of global solutions is discussed.

KW - Blow-up

KW - Coupled fractional-diffusion equations

KW - Global solution

KW - Polynomial nonlinearities

UR - https://www.scopus.com/pages/publications/85095809017

M3 - Article

AN - SCOPUS:85095809017

SN - 1072-6691

VL - 2020

SP - 1

EP - 28

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

M1 - 110

ER -

Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations

Abstract

Keywords

Other files and links

Fingerprint

Cite this