The Resource Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)

Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)

Label
Stochastic Partial Differential Equations: An Introduction
Title
Stochastic Partial Differential Equations: An Introduction
Statement of responsibility
by Wei Liu, Michael Röckner
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and the ‘locally monotone case’ is presented in a detailed and complete way for SPDEs. The extension to this more general framework for SPDEs, for example, in comparison to the well-known case of globally monotone coefficients, substantially widens the applicability of the results. In addition, it leads to a unified approach and to simplified proofs in many classical examples. These include a large number of SPDEs not covered by the ‘globally monotone case’, such as, for exa mple, stochastic Burgers or stochastic 2D and 3D Navier-Stokes equations, stochastic Cahn-Hilliard equations and stochastic surface growth models. To keep the book self-contained and prerequisites low, necessary results about SDEs in finite dimensions are also included with complete proofs as well as a chapter on stochastic integration on Hilbert spaces. Further fundamentals (for example, a detailed account on the Yamada-Watanabe theorem in infinite dimensions) used in the book have added proofs in the appendix. The book can be used as a textbook for a one-year graduate course
Member of
http://library.link/vocab/creatorName
Liu, Wei
Image bit depth
0
LC call number
  • QA273.A1-274.9
  • QA274-274.9
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Röckner, Michael.
  • SpringerLink
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Mathematics
  • Differential equations
  • Partial differential equations
  • Game theory
  • Mathematical physics
  • Probabilities
  • Mathematics
  • Probability Theory and Stochastic Processes
  • Partial Differential Equations
  • Ordinary Differential Equations
  • Mathematical Applications in the Physical Sciences
  • Game Theory, Economics, Social and Behav. Sciences
Label
Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Motivation, Aims and Examples -- Stochastic Integral in Hilbert Spaces -- SDEs in Finite Dimensions -- SDEs in Infinite Dimensions and Applications to SPDEs -- SPDEs with Locally Monotone Coefficients -- Mild Solutions
Dimensions
unknown
Edition
1st ed. 2015.
Extent
VI, 266 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783319223544
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-22354-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-22354-4
Label
Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Motivation, Aims and Examples -- Stochastic Integral in Hilbert Spaces -- SDEs in Finite Dimensions -- SDEs in Infinite Dimensions and Applications to SPDEs -- SPDEs with Locally Monotone Coefficients -- Mild Solutions
Dimensions
unknown
Edition
1st ed. 2015.
Extent
VI, 266 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783319223544
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-22354-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-22354-4

Library Locations

  • African Studies LibraryBorrow it
    771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Alumni Medical LibraryBorrow it
    72 East Concord Street, Boston, MA, 02118, US
    42.336388 -71.072393
  • Astronomy LibraryBorrow it
    725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US
    42.350259 -71.105717
  • Fineman and Pappas Law LibrariesBorrow it
    765 Commonwealth Avenue, Boston, MA, 02215, US
    42.350979 -71.107023
  • Frederick S. Pardee Management LibraryBorrow it
    595 Commonwealth Avenue, Boston, MA, 02215, US
    42.349626 -71.099547
  • Howard Gotlieb Archival Research CenterBorrow it
    771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Mugar Memorial LibraryBorrow it
    771 Commonwealth Avenue, Boston, MA, 02215, US
    42.350723 -71.108227
  • Music LibraryBorrow it
    771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Pikering Educational Resources LibraryBorrow it
    2 Silber Way, Boston, MA, 02215, US
    42.349804 -71.101425
  • School of Theology LibraryBorrow it
    745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350494 -71.107235
  • Science & Engineering LibraryBorrow it
    38 Cummington Mall, Boston, MA, 02215, US
    42.348472 -71.102257
  • Stone Science LibraryBorrow it
    675 Commonwealth Avenue, Boston, MA, 02445, US
    42.350103 -71.103784
Processing Feedback ...