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Stability and Pattern Formation in a General Class of Reaction-Diffusion-Advection System

Stability and Pattern Formation in a General Class of Reaction-Diffusion-Advection System In this paper, we systematically study two-species reaction-diffusion-advection system with linear cross-diffusion and cross-advection. Firstly, we provide sufficient conditions for cross-diffusion, self-advection and cross-advection driven instability, which implies that cross-diffusion, self-advection and cross-advection can give rise to pattern formation for the same diffusion coefficients. Secondly, we focuses on a class of general reaction-diffusion-advection system. By investigating the linearized stability of the constant equilibrium solution, we prove that the self-diffusion and self-advection terms have no effect on the stabilization of the constant steady state, the linear cross terms favor the destabilization of the constant steady state and mechanism of pattern formation. Furthermore, the theoretical results are applied to predator-prey and water-vegetation systems with cross-diffusion and cross-advection. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Stability and Pattern Formation in a General Class of Reaction-Diffusion-Advection System

Maimaiti, Yimamu; Yang, Wenbin
Acta Applicandae Mathematicae , Volume 185 (1) – Jun 1, 2023
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References (24)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-023-00576-4
Publisher site
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Abstract

In this paper, we systematically study two-species reaction-diffusion-advection system with linear cross-diffusion and cross-advection. Firstly, we provide sufficient conditions for cross-diffusion, self-advection and cross-advection driven instability, which implies that cross-diffusion, self-advection and cross-advection can give rise to pattern formation for the same diffusion coefficients. Secondly, we focuses on a class of general reaction-diffusion-advection system. By investigating the linearized stability of the constant equilibrium solution, we prove that the self-diffusion and self-advection terms have no effect on the stabilization of the constant steady state, the linear cross terms favor the destabilization of the constant steady state and mechanism of pattern formation. Furthermore, the theoretical results are applied to predator-prey and water-vegetation systems with cross-diffusion and cross-advection.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Jun 1, 2023

Keywords: Cross-diffusion; Cross-advection; Turing instability; Neutral curves; Vegetation patterns

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