The Fisher-KPP equation is a diffusion equation with logistic reaction modeling the time evolution of the density of one species confined in the bounded domain.
According to this interpretation, we expect that the density remains non-negative during the evolution. Despite in the continuous setting it is not difficult to prove this, at the discrete level the same results are not trivial at all.
During this talk, we discuss a numerical method preserving the entropy structure of the Fisher-KPP equation. With this structure, we can show that the density stays always non-negative and decays algebraically to the stable steady state of the Fisher-KKP equation.
This talk is based on a a joint work with Francesca Bonizzoni (University of Vienna), Ansgar Jüngel (Vienna University of technology) and Ilaria Perugia (University of Vienna).