In this lecture we will consider the recently developed theory of stochastic scalar conservation laws. A model example of this class of SPDE is given by the stochastic Burgers equation. In the first part of the lecture we will prove the well-posedness of entropy solutions to this class of SPDE. In spatially inhomogeneous cases this will rely on certain estimates from rough-path theory. In the second part of the lecture we will investigate the regularity properties of entropy and quasi-solutions to the stochastic Burgers equation. As a particularly interesting point we will observe that the regularity of quasi-solutions in the stochastic case is higher than what is true for deterministic scalar conservations laws.
| Rhythmus | Tag | Uhrzeit | Format / Ort | Zeitraum |
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| Studiengang/-angebot | Gültigkeit | Variante | Untergliederung | Status | Sem. | LP | |
|---|---|---|---|---|---|---|---|
| Bielefeld Graduate School in Theoretical Sciences / Promotion | |||||||
| Mathematik / Promotion | Subject-specific qualification | 1 | aktive Teilnahme | ||||
| Mathematik / Promotion | Subject-specific qualification | 1 | unbenotet |