A Hamilton-Jacobi approach for a model of population structured by space and trait


Sepideh Mirrahimi

11:30:00 - 12:20:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable and a phenotypical trait. Considering diffusion, mutations and competition between the individuals, we analyze the asymptotic (long–time/long–range in the space variable) behavior of the solutions. Using some kind of real phase WKB ansatz, we prove that the propagation of the population in space can be described by a Hamilton-Jacobi equation with obstacle which is independent of the trait variable. The effective Hamiltonian is derived from an eigenvalue problem which has a similar role as the cell problem in homogenization. Moreover, the eigenfunction corresponding to the latter eigenvalue problem provides a candidate for the phenotypical distribution of the population. This is a joint work with Emeric Bouin.

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