The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:257

Article

Li, Huicong¹  Wang, Xuefeng¹  Wu, Yanxia² 

[1] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

[2] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China

关键词: Logistic diffusion equation;    Coating;    Anisotropic diffusion tensor;    Effective boundary condition;    Lifespan;   

DOI  :  10.1016/j.jde.2014.07.004

来源: Elsevier

【 摘 要 】

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone. (C) 2014 Elsevier Inc. All rights reserved.

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