Thursday, July 13, 2023 - 14:30 in ZiF
The stochastic Klausmeier system: existence of a martingale solution
A talk in the SPDEs, optimal control and mean field games series by
Erika Hausenblas from Leoben
| Abstract: |
Nonlinear partial differential equations appear naturally in many biological
or chemical systems. E.g., activator-inhibitor systems play a role in morphogenesis
but also in ecology. The topic of the talk is a nonlinear partial differential
equation disturbed by stochastic noise. In particular, we show the existence
of a martingale solution to the stochastic Klausmeier system arising in ecology
using a stochastic version of a Tychanoff-Schauder type Theorem. Here we have
to mention that the stochastic Klausmeier system is not monotone, nor do they
satisfy a maximum principle. If there is some time, we will show also path wise
uniqueness in dimension one. This is a joint work with Jonas Tölle.
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