An Introduction to Singular Stochastic PDEs : Allen Cahn Equations, Metastability, and Regularity Structures
Stochastic partial differential equations (SPDEs) model the evolution in time of spatially extended systems subject to a random driving. Recent years have witnessed tremendous progress in the theory of so-called singular SPDEs. These equations feature a singular, distribution-valued driving term, a...
Enregistré dans:
| Auteur principal: | |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin :
European Mathematical Society
2022.
Berlin : |
| Collection: | EMS Series of Lectures in Mathematics
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| Sujets: | |
| Accès en ligne: | Accès sur la plateforme EMS Press Accès sur la plateforme ISTEX Accès Université d'Orléans Accès INSA CVL |
| Note: |
European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • An introduction to singular stochastic PDEs, Allen Cahn equations, metastability, and regularity structures, Nils Berglund, 2022, Berlin, European Mathematical Society, 1 volume (X-220 p.), EMS Series of Lectures in Mathematics, 978-3-98547-014-3 |
| Résumé: | Stochastic partial differential equations (SPDEs) model the evolution in time of spatially extended systems subject to a random driving. Recent years have witnessed tremendous progress in the theory of so-called singular SPDEs. These equations feature a singular, distribution-valued driving term, a typical example being spacetime white noise, which makes them ill-posed as such. In many cases, it is however possible to make sense of these equations by applying a so-called renormalisation procedure, initially introduced in quantum field theory. This book gives a largely self-contained exposition of the subject of regular and singular SPDEs in the particular case of the Allen Cahn equation, which models phase separation. Properties of the equation are discussed successively in one, two and three spatial dimensions, allowing to introduce new difficulties of the theory in an incremental way. In addition to existence and uniqueness of solutions, aspects of long-time dynamics such as invariant measures and metastability are discussed. A large part of the last chapter, about the three-dimensional case, is dedicated to the theory of regularity structures, which has been developed by Martin Hairer and co-authors in the last years, and allows to describe a large class of singular SPDEs. The book is intended for graduate students and researchers in mathematics and physics with prior knowledge in stochastic processes or stochastic calculus. |
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| Description: | European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| ISBN: | 9783985475148 |
| ISSN: | 2523-5184 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/wp-content/uploads/2022/07/EMS_ebooks_LN_CollEx_contrat.pdf |