##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Yuan Lou

#### Ohio State Unviersity

## Diffusion, advection, and geometry of population habitats

##### Abstract:

We will discuss the effects of advection along environmental gradients on logistic reaction-diffusion models for population growth. The local population growth rate is assumed to be spatially inhomogeneous, and the advection is taken to be a multiple of the gradient of the local population growth rate. We show that the effects of such advection depend crucially on the gemeotry of the habitats of population: if the habitat is convex, the movement in the direction of the gradient of the growth rate is beneficial to the population, while such advection could be harmful for certain non-convex habitats.

Host: Lei Ni

### April 16, 2003

### 4:00 PM

### AP&M 5829

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