Dalhousie-AARMS AAMP Seminar: Justin Tzou (Macquarie U.)

Title: Modeling and analysis of localized vegetation patterns on curved topography

Abstract: We propose a two-component reaction-advection-diffusion model for vegetation density and soil water concentration on a curved terrain which accounts for downhill flow of soil water, spatially dependent effective evaporation of soil water, and vertical rainfall on a curved surface. In the limit of slow diffusion of vegetation, we construct a one-spot localized solution corresponding to one patch of a periodic spotted vegetation pattern. We derive an ODE for the motion of the spot and determine how it is impacted by different aspects of the terrain. One such aspect is captured by the regular part of a certain Green’s function on the curved surface; I will briefly discuss how we numerically compute this quantity. Joint work with Leo Tzou.