On a reaction-diffusion-advection system : fixed boundary or free boundary

Xu, Ying and Zhu, Dandan and Ren, Jingli: On a reaction-diffusion-advection system : fixed boundary or free boundary.

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Abstract

This paper is devoted to the asymptotic behaviors of the solution to a reaction–diffusion–advection system in a homogeneous environment with fixed boundary or free boundary. For the fixed boundary problem, the global asymptotic stability of nonconstant semi-trivial states is obtained. It is also shown that there exists a stable nonconstant co-existence state under some appropriate conditions. Numerical simulations are given not only to illustrate the theoretical results, but also to exhibit the advection-induced difference between the left and right boundaries as time proceeds. For the free boundary problem, the spreading–vanishing dichotomy is proved, i.e., the solution either spreads or vanishes finally. Besides, the criteria for spreading and vanishing are further established.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 26
ISSN: 1417-3875
Page Range: pp. 1-31
Uncontrolled Keywords: Matematikai modell
Additional Information: Bibliogr.: p. 29-31. ; Összefoglalás angol nyelven
Date Deposited: 2018. Nov. 06. 11:54
Last Modified: 2020. Jul. 29. 12:29
URI: http://acta.bibl.u-szeged.hu/id/eprint/55696

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