Nonlinear stochastic evolution problems in applied sciences:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1992
|
| Series: | Mathematics and its applications
82 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 219 S. graph. Darst. |
| ISBN: | 0792320425 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONTENTS
Preface xi
Chapter 1 Stochastic Models and Random Evolution Equations 1
1.1 Introduction 1
1.2 A Classification of Partial Differential Equations 3
1.3 Function Spaces and the Definition of Solution 9
1.4 Stochastic Calculus of the Solution Process 12
1.5 Plan of the Book 20
References to Chapter 1 22
Chapter 2 Deterministic Systems with Random Initial Conditions 25
2.1 Introduction 25
2.2 Introduction to the Mathematical Problem 27
2.3 The Mathematical Method 29
2.4 Some Generalizations 39
2.5 Applications 49
References to Chapter 2 60
Chapter 3 The Random Initial Boundary Value Problem .... 63
3.1 Introduction 63
3.2 Mathematical Modelling in Stochastic Mechanics 64
3.3 The Mathematical Method 70
viii NONLINEAR STOCHASTIC EVOLUTION PROBLEMS
3.4 Problems in the Half Space and Problems in Several Space Variables . 75
3.5 The Random Heat Equation 77
3.6 Moving Boundary Problems in One Space Dimension 91
3.7 Final Discussion 93
References to Chapter 3 98
Chapter 4 Stochastic Systems with Additional Weighted Noise 101
4.1 Introduction 101
4.2 The Mathematical Model 103
4.3 Examples of Stochastic Partial Differential Equations in Mechanics . . 106
4.4 The Mathematical Method 117
4.5 Error Estimates 123
References to Chapter 4 130
Chapter 5 Time Evolution of the Probability Density .... 135
5.1 The First and Second Order Probability Densities 135
5.2 Deterministic Systems with Random Initial Conditions 137
; 5.3 Evolution of the Probability Density 143
5.4 On the Continuous Interpolation and Approximation of the
Probability Density and Entropy Functions 147
5.5 Systems with Random Initial Boundary Conditions and Parameters • 149
5.6 Application and Discussion 155
5.7 Some Conclusive Remarks 163
References to Chapter 5 164
Chapter 6 Some Further Developments of the SAI Method . 167
6.1 Introduction 167
6.2 Systems of Coupled Partial and Ordinary Differential Equations . . . 168
6.3 Integro Differential Equations 173
CONTENTS . —— ix
6.4 IU Posed Problems !74
6.5 Applications 181
6.6 Final Remarks 188
References to Chapter 6 188
Appendix : Basic Concepts of Probability Theory and Stochastic
Processes 191
References to Appendix 211
Authors Index 213
Subject Index 217
|
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV006813776 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:51:15Z |
| institution | BVB |
| isbn | 0792320425 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004317776 |
| oclc_num | 26809654 |
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| physical | XIV, 219 S. graph. Darst. |
| publishDate | 1992 |
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| publisher | Kluwer |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Bellomo, N. Verfasser aut Nonlinear stochastic evolution problems in applied sciences by N. Bellomo; Z. Brzezniak and L. M. de Socio Dordrecht u.a. Kluwer 1992 XIV, 219 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 82 Equations aux dérivées partielles stochastiques ram Equations différentielles non linéaires ram Differential equations, Nonlinear Stochastic partial differential equations Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 s DE-604 Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s DE-188 Brzeźniak, Zdzisław 1958- Verfasser (DE-588)120071193 aut De Socio, L. M. Verfasser aut Mathematics and its applications 82 (DE-604)BV008163334 82 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004317776&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bellomo, N. Brzeźniak, Zdzisław 1958- De Socio, L. M. Nonlinear stochastic evolution problems in applied sciences Mathematics and its applications Equations aux dérivées partielles stochastiques ram Equations différentielles non linéaires ram Differential equations, Nonlinear Stochastic partial differential equations Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4221363-0 (DE-588)4135969-0 |
| title | Nonlinear stochastic evolution problems in applied sciences |
| title_auth | Nonlinear stochastic evolution problems in applied sciences |
| title_exact_search | Nonlinear stochastic evolution problems in applied sciences |
| title_full | Nonlinear stochastic evolution problems in applied sciences by N. Bellomo; Z. Brzezniak and L. M. de Socio |
| title_fullStr | Nonlinear stochastic evolution problems in applied sciences by N. Bellomo; Z. Brzezniak and L. M. de Socio |
| title_full_unstemmed | Nonlinear stochastic evolution problems in applied sciences by N. Bellomo; Z. Brzezniak and L. M. de Socio |
| title_short | Nonlinear stochastic evolution problems in applied sciences |
| title_sort | nonlinear stochastic evolution problems in applied sciences |
| topic | Equations aux dérivées partielles stochastiques ram Equations différentielles non linéaires ram Differential equations, Nonlinear Stochastic partial differential equations Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Equations aux dérivées partielles stochastiques Equations différentielles non linéaires Differential equations, Nonlinear Stochastic partial differential equations Nichtlineare Evolutionsgleichung Stochastische partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004317776&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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