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Global existence and blow-up for a space and time nonlocal reaction-diffusion equation

Ahmed Alsaedi, Mokhtar Kirane and Berikbol Torebek (UGent)
(2021) QUAESTIONES MATHEMATICAE. 44(6). p.747-753
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Abstract
A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions is analysed.
Keywords
Mathematics (miscellaneous), Primary, Secondary, Caputo derivative, fractional Laplacian, reaction-diffusion equation, global existence, blow-up, REPRESENTATION, REGULARITY, STABILITY, Ghent Analysis & PDE center

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MLA
Alsaedi, Ahmed, et al. “Global Existence and Blow-up for a Space and Time Nonlocal Reaction-Diffusion Equation.” QUAESTIONES MATHEMATICAE, vol. 44, no. 6, 2021, pp. 747–53, doi:10.2989/16073606.2020.1745923.
APA
Alsaedi, A., Kirane, M., & Torebek, B. (2021). Global existence and blow-up for a space and time nonlocal reaction-diffusion equation. QUAESTIONES MATHEMATICAE, 44(6), 747–753. https://doi.org/10.2989/16073606.2020.1745923
Chicago author-date
Alsaedi, Ahmed, Mokhtar Kirane, and Berikbol Torebek. 2021. “Global Existence and Blow-up for a Space and Time Nonlocal Reaction-Diffusion Equation.” QUAESTIONES MATHEMATICAE 44 (6): 747–53. https://doi.org/10.2989/16073606.2020.1745923.
Chicago author-date (all authors)
Alsaedi, Ahmed, Mokhtar Kirane, and Berikbol Torebek. 2021. “Global Existence and Blow-up for a Space and Time Nonlocal Reaction-Diffusion Equation.” QUAESTIONES MATHEMATICAE 44 (6): 747–753. doi:10.2989/16073606.2020.1745923.
Vancouver
1.
Alsaedi A, Kirane M, Torebek B. Global existence and blow-up for a space and time nonlocal reaction-diffusion equation. QUAESTIONES MATHEMATICAE. 2021;44(6):747–53.
IEEE
[1]
A. Alsaedi, M. Kirane, and B. Torebek, “Global existence and blow-up for a space and time nonlocal reaction-diffusion equation,” QUAESTIONES MATHEMATICAE, vol. 44, no. 6, pp. 747–753, 2021.
@article{8713841,
  abstract     = {{A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions is analysed.}},
  author       = {{Alsaedi, Ahmed and Kirane, Mokhtar and Torebek, Berikbol}},
  issn         = {{1607-3606}},
  journal      = {{QUAESTIONES MATHEMATICAE}},
  keywords     = {{Mathematics (miscellaneous),Primary,Secondary,Caputo derivative,fractional Laplacian,reaction-diffusion equation,global existence,blow-up,REPRESENTATION,REGULARITY,STABILITY,Ghent Analysis & PDE center}},
  language     = {{eng}},
  number       = {{6}},
  pages        = {{747--753}},
  title        = {{Global existence and blow-up for a space and time nonlocal reaction-diffusion equation}},
  url          = {{http://doi.org/10.2989/16073606.2020.1745923}},
  volume       = {{44}},
  year         = {{2021}},
}
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