Niagara Falls, December 2 - 5, 2016
In the context of population dynamics, this initial value problem can be viewed as a model of a population undergoing Malthusian growth and spreading by a random diffusion with the drift $w$ . The growth is characterized by a death rate $\alpha$, birth rate $\beta$ and a gestation/maturation period $\tau$. The problem is: given coefficients $\alpha,\beta,w,\tau$ determine if the population invade the habitat or goes extinct.
In the drift-free case, a complete solution was given by Travis and Webb. We will show that in some cases the relation between $\alpha$ and $\beta$ plays the dominant role in the extinction of the population. However, in the opposite cases, the drift can help the population to survive.