Long time behavior of Robin boundary sub-diffusion equation with fractional partial derivatives of Caputo type in differential and difference settings
Hendy A.S. Zaky M.A. Abbaszadeh M.
December 2021Elsevier B.V.
Mathematics and Computers in Simulation
2021#1901370 - 1378 pp.
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.
Caputo time-fractional diffusion equation , Dissipativity , Grönwall inequalities , Numerical-dissipative scheme , Robin boundary
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Department of Computational Mathematics and Computer Science, Institute of Natural sciences and Mathematics, Ural Federal University, ul. Mira. 19, Yekaterinburg, 620002, Russian Federation
Department of Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt
Department of Applied Mathematics, Physics Division, National Research Centre, Dokki, 12622, Cairo, Egypt
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran
Department of Computational Mathematics and Computer Science
Department of Mathematics
Department of Applied Mathematics
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
Department of Applied Mathematics
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