Stefano Bruno - Optimal Regularity in Time and Space for Stochastic Porous Medium Equations
| Dates: | 29 November 2023 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Stefano Bruno (University of Edinburgh) will speak at the Probability seminar. (in-person)
Stochastic porous medium equations are well-studied models describing non-linear diffusion dynamics perturbed by noise. In this talk, we consider the noise to be multiplicative, white in time and coloured in space and the diffusion coefficients to be Hölder continuous. Our assumptions include the cases of smooth coefficients of, at most, linear growth as well as squareroot - coefficients relevant in population dynamics. Using the kinetic solution theory for conservation laws, we prove optimal regularity estimates consistent with the optimal regularity derived for the deterministic porous medium equation in Gess (JEMS, 2020) and Gess, Sauer, Tadmor (APDE, 2020) and the presence of the temporal white noise. The proof of our result relies on a significant adaptation of velocity averaging techniques from their usual L^1 context to the natural L^2 setting of the stochastic case. This is joint work with Benjamin Gess and Hendrik Weber.
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Max Newman Room G.107
Alan Turing Building
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