A non-standard evolution problem arising in population genetics

Details A non-standard evolution problem arising in population genetics A non-standard evolution problem arising in population genetics

2008-01-09

arxiv.org/abs/0801.1335v2

Mathematics

Analysis of PDEs

16 pages. Proposition 4 statement and proof corrected. Also a number of typos has been fixed

Scientific paper

We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries, supplemented by a pair of conservation laws. It is readily shown that no classical or standard weak solution definition yields solvability of the problem. We provide an appropriate definition of weak solution for the problem, for which we show existence and uniqueness. The solution displays a very distinctive structure and, for large time, we show convergence to a unique stationary solution that turns out to be a singular measure supported at the endpoints. An exponential rate of convergence to this steady state is also proved.

Affiliated with

Also associated with

No associations

Rating

A non-standard evolution problem arising in population genetics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A non-standard evolution problem arising in population genetics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A non-standard evolution problem arising in population genetics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-669299