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Session 23. Nonlinear Evolution Equations and their Applications
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Finite speed of propagation and waiting times for the stochastic porous medium equation - a unifying approach |
Günther Grün, University of Erlangen-Nürnberg, Germany
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The talk is based on a joint work with Julian Fischer (Zürich)
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We formulate a criterion on initial data which guarantees that
solutions to stochastic porous medium equations with linear
multiplicative noise exhibit a waiting time phenomenon almost
surely. Up to a logarithmic factor, it coincides with the optimal
criterion known from the deterministic setting. A novel iteration
technique and stochastic counterparts of weighted integral estimates
used in the deterministic setting - these are the key ingredients
of our approach, which may be modified to prove basic results on
finite speed of propagation, too.
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