The frequency-dependent Wright–Fisher model: diffusive and non-diffusive approximations

The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations.

We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the discrete problem, we are able to derive a corresponding continuous weak formulation for the probability density. Therefore, we obtain a family of partial different...

Diffusive Corrections to PN Approximations

In this paper, we investigate moment methods from a general point of view using an operator notation. This theoretical approach lets us explore the moment closure problem in more detail. This gives rise to a new idea, proposed in [14, 15], of how to improve the well-known PN approximations. We systematically develop a diffusive correction to the PN equations from the operator formulation — the ...

Transport approximations in partially diffusive media

This paper concerns the analysis of approximations of transport equations in diffusive media. Firstly, we consider a variational formulation for the first-order transport equation that has the correct diffusive behavior in the limit of small mean free paths. The associated bilinear form is shown to be coercive on a classical Hilbert space in transport theory with a constant of coercivity indepe...

Stable Non-gaussian Diffusive Profiles

We prove two stability results for the scale invariant solutions of the nonlinear heat equation ∂ t u = ∆u−|u| p−1 u with 1 < p < 1+ 2 n , n being the spatial dimension. The first result is that a small perturbation of a scale invariant solution vanishes as t → ∞. The second result is global, with a positivity condition on the initial data.

Convergence of Diffusive Bgk Approximations for Nonlinear Strongly Parabolic Systems