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Degenerate parabolic stochastic partial differential equations
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Researcher | Hofmanová, Martina |
| Date of Submission | 2013-07-05 |
| Abstract | In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the second part, we consider hyperbolic conservation laws with stochastic forcing and study their approximations in the sense of Bhatnagar-Gross-Krook. In particular, we describe the conservation laws as a hydrodynamic limit of the stochastic BGK model as the microscopic scale vanishes. In the last part, we provide a new and fairly elementary proof of Skorkhod's classical theorem on existence of weak solutions to SDEs with continuous coefficients satisfying a suitable Lyapunov condition. |
| File Format | |
| Language | French English |
| Publisher Institution | École normale supérieure de Cachan - ENS Cachan |
| Access Restriction | Open |
| Subject Keyword | Kinetic solutions Stochastic differential equations Stochastic partial differential equations Solutions cinétiques Équations différentielles stochastiques Équations aux dérivées partielles stochastiques math Mathematics [math] General Mathematics [math.GM] |
| Content Type | Text |
| Resource Type | Thesis |
