## Benoit Perthame
## AbstractABSTRACT
We wll give a mathematical model of such dynamics and show that an asymptotic method allows us to describe the evolution of the 'best adapted trait' and eventually to compute bifurcations which lead to the cohabitation of two different populations. In the regular regime, we obtain a canonical equation where the drift is given by a nonlinear problem. The asymptotic method leads to evaluate the weight and position of a moving Dirac mass describing the population. We will show that a Hamilton-Jacobi equation with constraints naturally describes this asymptotic. Some more theoretical questions as uniqueness for the limiting H.-J. equation will be addressed. This work is a collaboration with O. Diekmann, P.-E. Jabin, S. Mischler and G. Barles. |