Adjoint equations and analysis of complex systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1995
|
| Series: | Mathematics and its applications
295 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 466 S. |
| ISBN: | 0792330137 |
Staff View
MARC
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| 245 | 1 | 0 | |a Adjoint equations and analysis of complex systems |c by Guri I. Marchuk |
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Record in the Search Index
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| adam_text | Table of Contents
AUTHOR S PREFACE TO THE ENGLISH EDITION ix
INTRODUCTION 1
PART I. ADJOINT EQUATIONS AND PERTURBATION THEORY 7
CHAPTER 1. Main and Adjoint Equations. Perturbation Theory 9
1.1. Main and Adjoint Operators in Linear Problems.
Elements of Theory 9
1.2. Adjoint Operators in Spectral Problems. Fourier Method 22
1.3. Adjoint Equations and Functionals. Elements of Theory 28
1.4. Adjoint Equations and Importance of Information 38
1.5. Adjoint Equations and Perturbation Theory
for Linear Functionals 43
1.6. Simple Nonlinear Problems 50
1.7. Adjoint Equations for Non Stationary Problems 59
1.8. Adjoint Equations and Simple Inverse Problems 67
1.9. Perturbation Theory 76
1.10. Adjoint Equations. Perturbation Algorithms 86
1.11. Perturbation Algorithms for Eigenvalue Problems 88
CHAPTER 2. Simple Main and Adjoint Equations of Mathematical Physics 95
2.1. Diffusion Equation 95
2.2. Heat Conductivity Equation 104
2.3. Oscillation Equation 113
CHAPTER 3. Nonlinear Equations 123
3.1. Nonlinear Equations and Adjoint Problems 124
3.2. General Formulation of the Adjoint Problem 129
3.3. Small Perturbation Theory 130
3.4. Case of Problem with Perturbed Operator 138
3.5. On the Higher Order Perturbation Theory 145
3.6. Other Approaches to Construction of Adjoint Operators
in Nonlinear Problems 152
vi CONTENTS
CHAPTER 4. Inverse Problems and Adjoint Equations 164
4.1. Basic Definitions and Examples 165
4.2. Solution of Inverse Evolutionary Problems
with Constant Operators 173
4.3. Inverse Evolutionary Problem with Operator
Depending on Time 180
4.4. Statement of Inverse Problems on the Basis of Adjoint
Equation Methods and Perturbation Theory 187
4.5. Formulation of Perturbation Theory
for Complex Nonlinear Models 201
PART II. PROBLEMS OF ENVIRONMENT AND OPTIMIZATION
METHODS ON THE BASIS OF ADJOINT EQUATIONS 207
CHAPTER 5. Analysis of Mathematical Models in Environmental Problems 212
5.1. Atmospheric Pollutants Transport Equation.
Uniqueness of Solution 213
5.2. Stationary Equation for Propagation of Substances 217
5.3. Diffusion Approximation. Uniqueness of Solution 221
5.4. The Simple Diffusion Equation 230
5.5. Transport and Diffusion of Heavy Aerosols 235
5.6. The Structure and Modelling of Turbulent Motions
in the Atmosphere 237
5.7. Adjoint Equation for a Simple Diffusion Equation 242
5.8. General Case of Adjoint Problem for
Three Dimensional Domain 253
5.9. Uniqueness of Solution of Adjoint Problem 261
5.10. Adjoint Equation and Lagrange Identity 264
CHAPTER 6. Adjoint Equations, Optimization 269
6.1. Statement of the Problem 269
6.2. Adjoint Equations and Optimization Problem 276
6.3. Multi Criterial Optimization Problem 278
6.4. Problem of Minimax 281
6.5. Generalized Optimization Problem of Plant Location 282
6.6. Some General Remarks 284
6.7. Estimation of Biospherical Losses to Environment Pollution
by Industrial Emissions 289
6.8. Economics of Natural Resources 293
CONTENTS vii
6.9. Common Economic Criterion 296
6.10. Mathematical Problems of Optimization of Emissions
at Operating Industrial Plants 301
6.11. Perturbation Theory 307
6.12. Global Transport of Pollutants 310
CHAPTER 7. Adjoint Equations and Models of General Circulation
of Atmosphere and Ocean 326
7.1. Temperature Anomalies in the Atmosphere 328
7.2. Temperature anomalies in the Atmosphere and Ocean 341
7.3. Adjoint Functions of Atmosphere Dynamics 345
7.4. Adjoint Equations for Baroclinic Atmosphere 351
7.5. Baroclinic Model of the Atmosphere with a Heat Flux
from the Ocean 355
7.6. Problems of Climate Change Sensitivity in Various Regions
of the World 360
7.7. Application of the Sensitivity Theory to the Comparison
of Mathematical Models 381
CHAPTER 8. Adjoint Equations in Data Processing Problems 389
8.1. Data Assimilation Problem for Evolutionary Equation 390
8.2. Numerical Algorithm for Solving the Data Assimilation Problem 394
8.3. Numerical Method of Solution of Geophysical Data Assimilation
Problem Using the Splitting Scheme 400
8.4. Numerical Solution of Oceanic Data Initialization Problem 408
APPENDIX I: Splitting Methods in the Solution of Global Problems 422
1. Splitting Methods for Solution of Non Stationary Problems 422
2. Multicomponent Splitting of Problems 429
3. An Example of Application: Two Dimensional Problem
with Constant Coefficients 437
APPENDIX II: Difference Analogue of Non Stationary Heat Diffusion
Equation in Atmosphere and Ocean 441
BIBLIOGRAPHY 448
INDEX 464
|
| any_adam_object | 1 |
| author | Marčuk, Gurij I. 1925-2013 |
| author_GND | (DE-588)119060701 |
| author_facet | Marčuk, Gurij I. 1925-2013 |
| author_role | aut |
| author_sort | Marčuk, Gurij I. 1925-2013 |
| author_variant | g i m gi gim |
| building | Verbundindex |
| bvnumber | BV010198257 |
| classification_rvk | SK 500 SK 620 |
| classification_tum | MAT 418f MAT 344f |
| ctrlnum | (OCoLC)832292323 (DE-599)BVBBV010198257 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010198257 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:17Z |
| institution | BVB |
| isbn | 0792330137 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006776908 |
| oclc_num | 832292323 |
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| owner | DE-12 DE-703 DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-12 DE-703 DE-91G DE-BY-TUM DE-11 |
| physical | VII, 466 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Marčuk, Gurij I. 1925-2013 Verfasser (DE-588)119060701 aut Adjoint equations and analysis of complex systems by Guri I. Marchuk Dordrecht u.a. Kluwer 1995 VII, 466 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 295 Adjungierte Differentialgleichung (DE-588)4401337-1 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Adjungierte Differentialgleichung (DE-588)4401337-1 s Differenzierbares dynamisches System (DE-588)4137931-7 s Störungstheorie (DE-588)4128420-3 s DE-604 Mathematics and its applications 295 (DE-604)BV008163334 295 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006776908&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marčuk, Gurij I. 1925-2013 Adjoint equations and analysis of complex systems Mathematics and its applications Adjungierte Differentialgleichung (DE-588)4401337-1 gnd Störungstheorie (DE-588)4128420-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4401337-1 (DE-588)4128420-3 (DE-588)4137931-7 |
| title | Adjoint equations and analysis of complex systems |
| title_auth | Adjoint equations and analysis of complex systems |
| title_exact_search | Adjoint equations and analysis of complex systems |
| title_full | Adjoint equations and analysis of complex systems by Guri I. Marchuk |
| title_fullStr | Adjoint equations and analysis of complex systems by Guri I. Marchuk |
| title_full_unstemmed | Adjoint equations and analysis of complex systems by Guri I. Marchuk |
| title_short | Adjoint equations and analysis of complex systems |
| title_sort | adjoint equations and analysis of complex systems |
| topic | Adjungierte Differentialgleichung (DE-588)4401337-1 gnd Störungstheorie (DE-588)4128420-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Adjungierte Differentialgleichung Störungstheorie Differenzierbares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006776908&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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