Asymptotic dynamics of a population density: a model with a survival threshold
Seminar Room 1, Newton Institute
We study the long time-long range behavior of reaction diffusion equations with negative square-root reaction terms. In particular we investigate the exponential behavior of the solutions after a standard hyperbolic scaling. This leads to a Hamilton-Jacobi equality with an obstacle that depends on the solution itself. Our motivation comes from the so-called “tail problem” in population biology. We impose extra-mortality below a given survival threshold to avoid meaningless exponential tails. This is a joint work with G. Barles, B. Perthame and P. E. Souganidis.