WAVE PROPAGATION AND PATTERN FORMATION FOR A REACTION-DIFFUSION SYSTEM WITH NONLINEAR DIFFUSION
- Autori: Gambino, G.; Lombardo, M.; Sammartino, M.
- Anno di pubblicazione: 2008
- Tipologia: Altro
- Parole Chiave: Pattern, Ginzburg-Landau equation
- OA Link: http://hdl.handle.net/10447/39997
We investigate the formation of macroscopic spatio-temporal structures (patterns) for a reaction-diffusion system with nonlinear diffusion. We show that cross-diffusion effects are responsible of pattern initiation. Through a weakly nonlinear analysis we are able to predict the shape and the amplitude of the pattern. In the weakly nonlinear regime we derive the Ginzburg-Landau equation which captures the envelope evolution and the progressing of the pattern as a wave. Numerical simulations, performed using both a particle and a spectral method, are in good agreement with the analytical results.