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分析与微分方程研讨会

Derivation of a field-road model

Speaker

王学锋 , 香港中文大学(深圳)

Time

21 Nov, 10:45 - 11:30

Abstract

Of concern is the scenario of a road running through a large field, in which a diffusive species has different diffusion rates on the road and in the field, respectively. 8 years ago, Beresticky and collaborators proposed a field-road model, which consists of the KPP equation for the areal density function in the field, and a reaction-diffusion equation for the linear density function on the road (the x-axis), with the two density functions coupled by a Robin boundary on the x-axis. We wonder if this model can be derived from a more basic model. Indeed, we do so by first assuming the width of the road is positive, and then proposing a full model on the whole plane, with reasonable transmission conditions on the edges of the road, we then send the width of the road to 0. The resulting limiting model covers the field-road of Beresticky et al, and more. This is a joint work of Haomin Huang, Siyu Liu and Yantao Wang.