Global Existence and Blow-up of Solutions for a System of Fractional Wave Equations

Bashir Ahmad; Ahmed Alsaedi; Mohamed Berbiche; Mokhtar Kirane

doi:10.11650/tjm/210804

Global Existence and Blow-up of Solutions for a System of Fractional Wave Equations

Bashir Ahmad
, Ahmed Alsaedi
, Mohamed Berbiche
, Mokhtar Kirane

Mathematics

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

4 Scopus citations

Abstract

We investigate the Cauchy problem for a 2 × 2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in ℝ⁺×ℝ^N. Under appropriate conditions on the exponents and the fractional orders of the time derivatives, it is shown that there exists a threshold value of the dimension N, for which, small data-global solutions as well as finite time blowing-up solutions exist. Furthermore, we investigate the L^∞-decay estimates of global solutions.

Original language	British English
Pages (from-to)	103-135
Number of pages	33
Journal	Taiwanese Journal of Mathematics
Volume	26
Issue number	1
DOIs	https://doi.org/10.11650/tjm/210804
State	Published - Feb 2022

Keywords

blow-up
coupled fractional-wave equations
global solution
polynomial nonlinearities

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title = "Global Existence and Blow-up of Solutions for a System of Fractional Wave Equations",

abstract = "We investigate the Cauchy problem for a 2 × 2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in ℝ+×ℝN. Under appropriate conditions on the exponents and the fractional orders of the time derivatives, it is shown that there exists a threshold value of the dimension N, for which, small data-global solutions as well as finite time blowing-up solutions exist. Furthermore, we investigate the L∞-decay estimates of global solutions.",

keywords = "blow-up, coupled fractional-wave equations, global solution, polynomial nonlinearities",

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

note = "Funding Information: This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (KEP-PHD-80-130-42). The authors, therefore, acknowledge with thanks DSR technical and financial support. Publisher Copyright: {\textcopyright} 2022, Mathematical Society of the Rep. of China. All rights reserved.",

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AU - Alsaedi, Ahmed

AU - Berbiche, Mohamed

AU - Kirane, Mokhtar

N1 - Funding Information: This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (KEP-PHD-80-130-42). The authors, therefore, acknowledge with thanks DSR technical and financial support. Publisher Copyright: © 2022, Mathematical Society of the Rep. of China. All rights reserved.

PY - 2022/2

Y1 - 2022/2

N2 - We investigate the Cauchy problem for a 2 × 2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in ℝ+×ℝN. Under appropriate conditions on the exponents and the fractional orders of the time derivatives, it is shown that there exists a threshold value of the dimension N, for which, small data-global solutions as well as finite time blowing-up solutions exist. Furthermore, we investigate the L∞-decay estimates of global solutions.

AB - We investigate the Cauchy problem for a 2 × 2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in ℝ+×ℝN. Under appropriate conditions on the exponents and the fractional orders of the time derivatives, it is shown that there exists a threshold value of the dimension N, for which, small data-global solutions as well as finite time blowing-up solutions exist. Furthermore, we investigate the L∞-decay estimates of global solutions.

KW - blow-up

KW - coupled fractional-wave equations

KW - global solution

KW - polynomial nonlinearities

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SN - 1027-5487

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EP - 135

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

IS - 1

ER -

Global Existence and Blow-up of Solutions for a System of Fractional Wave Equations

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