Applied Analysis Seminar - Abstracts
Talk
Tuesday, 15 October 2019, 13:30-14:30 in HG00.310
Erika Hausenblas (University of Leoben)
The Stochastic Gray Scott system
Abstract
Reaction and diffusion of chemical species can produce a variety of patterns,
reminiscent of those often seen in nature. The Gray Scott system is a coupled
equation of reaction-diffusion type, modelling these kinds of patterns.
Depending on the parameter, stripes, waves, cloud streets, or sand ripples may appear.
These systems are the macroscopic model of microscopic dynamics.
Here, in the derivation of the equation, the random fluctuation of the molecules are neglected.
Adding a stochastic noise, the inherent randomness
of the microscopic behaviour is modelled. In particular, we add a time homogenous spatial
Gaussian random field with
a given spectral measure.
In the talk, we present our main result about the stochastic Gray Scott system.
In addition, we introduce and explain an algorithm for its numerical approximation
by operator splitting methods. Finally, we present some examples illustrating the
dynamical behaviour of the stochastic Gray Scott system.
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