Pattern formation of a biomass–water reaction–diffusion model. (January 2022)

• Record Type: Journal Article
• Authors: Lei, Chengxia; Zhang, Guanghui; Zhou, Jialin
• Is Part Of: Applied mathematics letters. Volume 123(2022)
• Publication Date: 2022-01
• Subjects: A biomass–water reaction–diffusion model -- Non-constant stationary solution -- Turing pattern -- Small/large diffusion; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107605
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.