An Introduction to Singular Stochastic PDEs | Allen-Cahn Equations, Metastability, and Regularity Structures
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| Title: | An Introduction to Singular Stochastic PDEs | Allen-Cahn Equations, Metastability, and Regularity Structures |
|---|---|
| Description: | 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. |
| Authors: | Nils Berglund |
| Resource Type: | eBook. |
| Subjects: | Stochastic partial differential equations, Stability |
| Categories: | MATHEMATICS / Probability & Statistics / Stochastic Processes, MATHEMATICS / Differential Equations / Partial |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: An Introduction to Singular Stochastic PDEs | Allen-Cahn Equations, Metastability, and Regularity Structures – Name: Abstract Label: Description Group: Ab Data: 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. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Nils+Berglund%22">Nils Berglund</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Stochastic+partial+differential+equations%22">Stochastic partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Stability%22">Stability</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Probability+%26+Statistics+%2F+Stochastic+Processes%22">MATHEMATICS / Probability & Statistics / Stochastic Processes</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Differential+Equations+%2F+Partial%22">MATHEMATICS / Differential Equations / Partial</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 519.22 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Stochastic partial differential equations Type: general – SubjectFull: Stability Type: general Titles: – TitleFull: An Introduction to Singular Stochastic PDEs | Allen-Cahn Equations, Metastability, and Regularity Structures Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Nils Berglund – PersonEntity: Name: NameFull: Nils Berglund IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2022 – D: 22 M: 10 Type: profile Y: 2022 Identifiers: – Type: isbn-print Value: 9783985470143 – Type: isbn-electronic Value: 9783985475148 Titles: – TitleFull: An Introduction to Singular Stochastic PDEs | Allen-Cahn Equations, Metastability, and Regularity Structures Type: main |
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