Wednesday, November 24, 2021 - 14:00 in ZOOM - Video Conference
Stochastic Generalized Porous Media Equations over $\sigma$-finite Measure Spaces with Non-continuous Nonlinearity
A talk in the Bielefeld Stochastic Afternoon series by
Weina Wu
| Abstract: |
This talk will be held via Zoom (for details email stochana(at)math.uni-bielefeld.de).
We prove that stochastic porous media equations over $\sigma$-finite measure spaces $(E,\mathcal{B},\mu)$, driven by time-dependent multiplicative noise, with the Laplacian replaced by a self-adjoint transient Dirichlet operator $L$ and the nonlinearity given by a maximal monotone multi-valued function $\Psi$ of polynomial growth, have a unique solution. This generalizes previous results in that we work on general measurable state spaces, allow non-continuous (nonlinear) monotone functions $\Psi$, for which, no further coercivity assumptions are needed, but only that their multi-valued extensions are maximal monotone and of at most polynomial growth. The result in particular applies to cases where $E$ is a manifold or a fractal, and to non-local operators $L$, as e.g. $L=-(-\Delta)^\alpha$, $\alpha\in(0,\frac{d}{2})\cap(0,1]$. This talk is based on a joint work with Michael Röckner and Yingchao Xie.
Within the CRC this talk is associated to the project(s): A5, B1 |
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