Long time behavior of Robin boundary sub-diffusion equation with fractional partial derivatives of Caputo type in differential and difference settings

Ahmed S. Hendy, Mahmoud A. Zaky and Mostafa Abbaszadeh

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 1370-1378

Abstract: A Robin boundary sub-diffusion equation is considered with fractional partial derivatives of the Caputo type. The model is an extension of various well-known equations from mathematical physics, biology, and chemistry. Initial–boundary data are imposed upon a closed and bounded spatial domain. We state and prove two main theorems in differential and difference settings to ensure the algebraic decay rate of the long-time behavior for that kind of problem. The dissipation of the continuous solution for such a problem is discussed in the first theorem based on energy inequalities and by the aid of Grönwall inequalities. It demonstrates that with an L2(Ω)-bounded absorbing set, the solution is dissipated with respect to time. The numerical dissipativity is proved in the second theorem by using discrete energy inequalities and the discrete Paley–Wiener inequality. Finally, an example is provided to illustrate the main outcomes.

Keywords: Caputo time-fractional diffusion equation; Robin boundary; Dissipativity; Numerical-dissipative scheme; Grönwall inequalities (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475421002561
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:1370-1378

DOI: 10.1016/j.matcom.2021.07.006

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().