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.

中文翻译：

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生物质-水反应-扩散模型的模式形成

在本文中，我们关注服从均匀 Neumann 边界条件的生物质-水反应-扩散模型。我们推导出关于大或小扩散率的非常数平稳解的存在和不存在的几个充分条件，这给出了该系统中图灵模式的可能性的标准。我们的结果证实了 Manor 和 Shnerb (2006) 的数值发现，并补充了 Wang 等人 (2017) 对相应 ODE 模型的理论结果。