| 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 kind 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 inherit randomness
of the microscopic behaviour is modelled. In particular, we add a time homogenous spatial Gaussian random field with given spectral measure.
In the talk, first the Gray Scott system is motivated. Then, then stochastic system is introduced and the question of existence and uniqueness are addressed.
In the second part of the talk, we present some numerical simulations and the corresponding adapted approximation scheme is explained.
Finally, some extension and generalization of the result are presented. |
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