Seminár z kvalitatívnej teórie diferenciálnych rovníc - Richard Kollár (21.4.2016)

vo štvrtok 21.4.2016 o 14:00 hod. v miestnosti M/223

13. 04. 2016 12.53 hod.
Od: Pavol Quittner

Prednášajúci: Richard Kollár

Názov: Existence and stability of traveling waves for generalized FKPP equation

Termín: 21.4.2016, 14:00, M/223

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).