Softcover ISBN:  9783985470143 
Product Code:  EMSSERLEC/34 
List Price:  $49.00 
AMS Member Price:  $39.20 
Softcover ISBN:  9783985470143 
Product Code:  EMSSERLEC/34 
List Price:  $49.00 
AMS Member Price:  $39.20 

Book DetailsEMS Series of Lectures in MathematicsVolume: 34; 2022; 232 ppMSC: Primary 60; 81; 35
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 socalled singular SPDEs. These equations feature a singular, distributionvalued driving term, a typical example being spacetime white noise, which makes them illposed as such. In many cases, however, it is possible to make sense of these equations by applying a socalled renormalization procedure, initially introduced in quantum field theory.
This book gives a largely selfcontained exposition of the subject of regular and singular SPDEs in the particular case of the AllenCahn equation, which models phase separation. Properties of the equation are discussed successively in one, two, and three spatial dimensions, allowing the author to introduce new difficulties of the theory in an incremental way. In addition to existence and uniqueness of solutions, aspects of longtime dynamics, such as invariant measures and metastability, are discussed. A large part of the last chapter about the threedimensional case is dedicated to the theory of regularity structures, which has been developed by Martin Hairer and coauthors in the last years, and makes it possible 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.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipGraduate students and researchers interested in probability theory and stochastic partial differential equations.

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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 socalled singular SPDEs. These equations feature a singular, distributionvalued driving term, a typical example being spacetime white noise, which makes them illposed as such. In many cases, however, it is possible to make sense of these equations by applying a socalled renormalization procedure, initially introduced in quantum field theory.
This book gives a largely selfcontained exposition of the subject of regular and singular SPDEs in the particular case of the AllenCahn equation, which models phase separation. Properties of the equation are discussed successively in one, two, and three spatial dimensions, allowing the author to introduce new difficulties of the theory in an incremental way. In addition to existence and uniqueness of solutions, aspects of longtime dynamics, such as invariant measures and metastability, are discussed. A large part of the last chapter about the threedimensional case is dedicated to the theory of regularity structures, which has been developed by Martin Hairer and coauthors in the last years, and makes it possible 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.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Graduate students and researchers interested in probability theory and stochastic partial differential equations.