Pattern formation of a biomass–water reaction–diffusion model

In this paper, we are concerned with a biomass–water reaction–diffusion model subject to the homogeneous Neumann boundary condition. We derive several sufficient conditions on the existence and non-existence of non-constant stationary solutions with respect to large or small diffusion rate, which gi...

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Bibliographic Details
Published inApplied mathematics letters Vol. 123; p. 107605
Main Authors Lei, Chengxia, Zhang, Guanghui, Zhou, Jialin
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.01.2022
Subjects
A biomass–water reaction–diffusion model
Non-constant stationary solution
Small/large diffusion
Turing pattern
Small/large diffusion
Non-constant stationary solution
A biomass–water reaction–diffusion model
Turing pattern
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Summary:In this paper, we are concerned with a biomass–water reaction–diffusion model subject to the homogeneous Neumann boundary condition. We derive several sufficient conditions on the existence and non-existence of non-constant stationary solutions with respect to large or small diffusion rate, which give the criteria for the possibility of Turing patterns in this system. Our results confirm the numerical findings of Manor and Shnerb, (2006) and also complement the theoretical results of Wang et al., (2017) for the corresponding ODE model.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2021.107605