Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method

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Benito, J. J. and García, A. and Gavete, L. and Negreanu, Mihaela and Ureña, F. and Vargas, A. M. (2020) Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method. Applied Numerical Mathematics, 157 . pp. 356-371. ISSN 0168-9274

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Official URL: https://doi.org/10.1016/j.apnum.2020.06.011



Abstract

This work studies a parabolic-parabolic chemotactic PDE's system which describes the evolution of a biological population “U” and a chemical substance “V”, using a Generalized Finite Difference Method, in a two dimensional bounded domain with regular boundary. In a previous paper [12], the authors asserted global classical solvability and periodic asymptotic behavior for the continuous system in 2D. In this continuous work, a rigorous proof of the global classical solvability to the discretization of the model proposed in [12] is presented in two dimensional space. Numerical experiments concerning the convergence in space and in time, and long-time simulations are presented in order to illustrate the accuracy, efficiency and robustness of the developed numerical algorithms.


Item Type:Article
Uncontrolled Keywords:Generalized Finite; Difference Meshless method; Chemotaxis system
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:74745
Deposited On:23 Sep 2022 10:50
Last Modified:23 Sep 2022 11:34

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