Stochastic partial differential equations: an introduction
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Cham ; Heidelberg ; New York ; Dordrecht ; London
Springer
[2015]
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Datensatz im Suchindex
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| adam_text | STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS: AN INTRODUCTION
/ LIU, WEI
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS: AN INTRODUCTION
/ LIU, WEI
: 2015
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Liu, Wei Röckner, Michael 1956- |
| author_GND | (DE-588)1081959584 (DE-588)121250199 |
| author_facet | Liu, Wei Röckner, Michael 1956- |
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| author_variant | w l wl m r mr |
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| classification_tum | MAT 000 |
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-22354-4 |
| format | Electronic eBook |
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| indexdate | 2024-12-24T04:48:32Z |
| institution | BVB |
| isbn | 9783319223544 |
| issn | 0172-5939 |
| language | English |
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| spellingShingle | Liu, Wei Röckner, Michael 1956- Stochastic partial differential equations: an introduction Mathematics Differential equations Partial differential equations Game theory Mathematical physics Probabilities Probability Theory and Stochastic Processes Partial Differential Equations Ordinary Differential Equations Mathematical Applications in the Physical Sciences Game Theory, Economics, Social and Behav. Sciences Mathematik Mathematische Physik Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4135969-0 (DE-588)4151278-9 |
| title | Stochastic partial differential equations: an introduction |
| title_auth | Stochastic partial differential equations: an introduction |
| title_exact_search | Stochastic partial differential equations: an introduction |
| title_full | Stochastic partial differential equations: an introduction Wei Liu, Michael Röckner |
| title_fullStr | Stochastic partial differential equations: an introduction Wei Liu, Michael Röckner |
| title_full_unstemmed | Stochastic partial differential equations: an introduction Wei Liu, Michael Röckner |
| title_short | Stochastic partial differential equations: an introduction |
| title_sort | stochastic partial differential equations an introduction |
| topic | Mathematics Differential equations Partial differential equations Game theory Mathematical physics Probabilities Probability Theory and Stochastic Processes Partial Differential Equations Ordinary Differential Equations Mathematical Applications in the Physical Sciences Game Theory, Economics, Social and Behav. Sciences Mathematik Mathematische Physik Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Mathematics Differential equations Partial differential equations Game theory Mathematical physics Probabilities Probability Theory and Stochastic Processes Partial Differential Equations Ordinary Differential Equations Mathematical Applications in the Physical Sciences Game Theory, Economics, Social and Behav. Sciences Mathematik Mathematische Physik Stochastische partielle Differentialgleichung Einführung |
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