### Seminar 21.4.2016: Richard Kollar

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**Tue Apr 12, 2016 3:13 pm**Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 21.4.2016 at 14:00 Lecture room M-223

Richard Kollár (KAMŠ FMFI UK):

Existence and stability of traveling waves for generalized FKPP equation

Abstrakt:

The well-known Fisher-Kolmogorov-Piskunov-Petrovsky (FKPP) equation was originally

derived by Fisher to model spatial propagation of advantageous genes in population.

However, evidence shows that the dispersal and mean convection of individuals

is gene-dependent and thus the model needs to be reformulated as a system

for different genotypes with different diffusion and convection coefficients.

Under an assumption of a constant population the system can be rephrased

as a single generalized FKPP equation. We show that similarly to the FKPP equation

it supports existence of traveling waves for an interval of admissible wave speeds.

We also study stability of such traveling waves.

This is a joint work with Sebastian Novak (IST Austria).

Seminar on Qualitative Theory of Differential Equations

Thursday 21.4.2016 at 14:00 Lecture room M-223

Richard Kollár (KAMŠ FMFI UK):

Existence and stability of traveling waves for generalized FKPP equation

Abstrakt:

The well-known Fisher-Kolmogorov-Piskunov-Petrovsky (FKPP) equation was originally

derived by Fisher to model spatial propagation of advantageous genes in population.

However, evidence shows that the dispersal and mean convection of individuals

is gene-dependent and thus the model needs to be reformulated as a system

for different genotypes with different diffusion and convection coefficients.

Under an assumption of a constant population the system can be rephrased

as a single generalized FKPP equation. We show that similarly to the FKPP equation

it supports existence of traveling waves for an interval of admissible wave speeds.

We also study stability of such traveling waves.

This is a joint work with Sebastian Novak (IST Austria).