Applied theory of functional differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1992
|
| Series: | Mathematics and its applications / Soviet series
85 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 234 S. graph. Darst. |
| ISBN: | 0792320131 |
Staff View
MARC
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| 245 | 1 | 0 | |a Applied theory of functional differential equations |c by V. Kolmanovskii and A. Myshkis |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1992 | |
| 300 | |a XV, 234 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics and its applications / Soviet series |v 85 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xiii
Chapter 1. Models 1
1. Formal prerequisites 1
1.1. Functional differential equations 1
1.2. Solution concept for a FDE 2
1.3. FDE with aftereffect 4
1.4. A little bit of philosophy 7
2. Aftereffect in mechanics 10
2.1. Viscoelasticity 10
2.2. Models of motion with aftereffect 11
2.3. Controlled motion of a rigid body 13
2.4. Models of polymer crystallization 14
2.5. Stretching of a polymer filament 14
3. Hereditary phenomena in physics 15
3.1. Dynamics of oscillators 15
3.2. Relativistic dynamics 15
3.3. Nuclear reactors 16
3.4. Distributed networks (long line with tunnel diode) 16
3.5. Heat flow in materials with memory 18
3.6. Models of lasers 18
4. Models with delays in technical problems 18
4.1. Infeed grinding and cutting 18
4.2. Technological delay 20
4.3. Car chasing 21
4.4. Ship course stabilization 21
vii
viii CONTENTS
5. Aftereffect in biology 21
5.1. Evolution equations of a single species 22
5.2. Interaction of two species 24
5.3. Population dynamics model of N interacting species 24
5.4. Coexistence of competitive micro organisms 25
5.5. Control problems in ecology 25
5.6. Control problems in microbiology 26
5.7. Nicholson blowflies model 27
5.8. Helical movement of tips of growing plants 27
6. Aftereffect in medicine 27
6.1. Mathematical models of the sugar quantity in blood 27
6.2. Model of arterial blood pressure regulation 28
6.3. Cancer chemotherapy 30
6.4. Mathematical models of learning 30
6.5. Mathematical models in immunology and epidemiology 30
6.6. Model of the human immunodeficiency virus (HIV) epidemic 31
6.7. Model of survival of red blood cells 32
6.8. Vision process in the compound eye 32
7. Aftereffect in economy and other sciences 32
7.1. Optimal skill with retarded controls 33
7.2. Optimal advertising policies 33
7.3. Commodity price fluctuations 34
7.4. Model of the fishing process 34
7.5. River pollution control 34
Chapter 2. General theory 35
1. Introduction. Method of steps 35
1.1. Notation 35
1.2. Cauchy problem for FDEs 36
1.3. Step method for RDEs 36
1.4. Step methods for NDEs 38
1.5. Problems for a process with aftereffect renewal 39
2. Cauchy problem for RDEs 40
2.1. Basic solvability theorem 40
2.2. Variants 41
2.3. Semigroup relation 43
2.4. Absolutely continuous solutions 44
2.5. RDEs with infinite delay 45
2.6. Properties of the Cauchy problem for RDEs 46
CONTENTS ix
3. Cauchy problem for NDEs 48
3.1. Smooth solutions 48
3.2. NDEs with functional of integral type 49
3.3. Application of the step method 51
3.4. Transition to an operator equation 52
3.5. Hale s form of NDEs 54
4. Differential inclusions of retarded type (RDIs) 55
4.1. Introduction 55
4.2. Multimaps 56
4.3. Solvability of the Cauchy problem for RDIs 57
4.4. Generalized solutions of RDEs and RDIs 58
5. General linear equations with aftereffect 62
5.1. Cauchy problem for linear RDEs 62
5.2. Generalization 63
5.3. Integral representation for the solution of the Cauchy problem (varia¬
tion of constants formula) 65
5.4. Adjoint equation. Periodic solutions u 7
5.5. Neutral type equations (NDEs) 68
6. Linear autonomous equations 70
6.1. Exponential solutions of linear autonomous RDEs 70
6.2. Solution of the Cauchy problem 72
6.3. Example of a showering person 74
6.4. Linear autonomous NDEs 78
7. Hopf bifurcation 80
7.1. Introduction 80
7.2. Example 81
7.3. General case 85
7.4. Variants 87
7.5. Example of an RDE with constant delay: intraspecial struggle for a
common food 89
7.6. Example of an RDE with autoregulative delay: combustion in the
chamber of a turbojet engine 90
7.7. Example NDE: auto oscillation in a long line with tunnel diod 92
8. Stocnastic retarded differential equations (SRDEs) 92
8.1. Initial value problem 93
8.2. Existence and uniqueness of solutions 94
8.3. Some characteristics of solutions of linear equations 95
x CONTENTS
Chapter 3. Stability of retarded differential equations 97
1. Liapunov s direct method 97
1.1. Stability definitions 97
1.2. Stability theorems for equations with bounded delay 100
1.3. Stability of equations with unbounded delay 105
1.4. Stability of linear nonautonomous equations 108
1.5. Stability of linear periodic differential equations 109
1.6 Application of comparison theorems 109
1.7. Stability in the first approximation 110
1.8. Instability 111
2. Linear autonomous equations 112
2.1. General stability conditions 112
2.2. Scalar nth order equations 114
2.3. Equations with discrete delays 116
Chapter 4. Stability of neutral type functional differential equations 125
1. Direct Liapunov s method 125
1.1. Degenerate Liapunov functionals 125
1.2. Stability in a first approximation 128
1.3. The use of functionals depending on derivatives 129
2. Stability of linear autonomous equations 130
2.1. General case 130
2.2. Scalar equations 131
2.3. Stability of NFDEs with discrete delays 133
2.4. The influence of small delays on stability 135
Chapter 5. Stability of stochastic functional differential equations 137
1. Statement of the problem 137
1.1. Definitions of stability 137
1.2. Ito s formula 138
2. Liapunov s direct method 139
2.1. Asymptotic stability 139
2.2. Examples I40
2.3. Exponential stability 143
2.4. Stability in the first approximation 143
2.5. Stability under persistent disturbances 144
3. Boundedness of moments of solutions 145
3.1. General conditions for boundedness of moments 145
3.2. Scalar equations 146
3.3. Second order equations 148
CONTENTS xi
Chapter 6. Problems of control for deterministic FDEs 151
1. The dynamic programming method for deterministic equations.
Bellman s equation 151
1.1. Statement of the problem 151
1.2. Optimality conditions 153
2. Linear quadratic problems 153
2.1. Optimal control synthesis 153
2.2. Exact solution 155
2.3. Systems with delays in the control 155
2.4. Effects of delays in regulators 157
2.5. Neutral type equations 158
3. Optimal control of bilinear hereditary systems 159
3.1. Optimality conditions 159
3.2. Construction of the optimal control synthesis 160
3.3. Model of optimal feedback control for microbial growth 162
4. Control problems with phase constraint formula 162
4.1. General optimality conditions 162
4.2. Equations with discrete delays 164
5. Necessary optimality conditions 166
5.1. Systems with state delays 166
5.2. Systems with delays in the control 168
5.3. Systems with distributed delays 169
5.4. Linear systems with discrete and distributed delays 170
5.5. Neutral type systems 171
Chapter 7. Optimal control of stochastic delay systems 173
1. Dynamic programming method for controlled stochastic hereditary
processes 173
1.1. Problem statement 173
2. The linear quadratic problem 174
2.1. Bellman functional and optimal control 174
2.2. Approximate solution 175
2.3. Some generalizations 176
3. Approximate optimal control for systems with small parameters 177
3.1. Formal algorithm 177
3.2. Quasilinear systems with quadratic cost 178
4. Another approach to the problem of optimal synthesis control 179
4.1. Admissible functionals 180
4.2. Quasilinear quadratic problems 180
xii CONTENTS
Chapter 8. State estimates of stochastic systems with delay 183
1. Filtering of Gaussian processes 183
1.1. Problem statement 183
1.2. Integral representation for the optimal estimate 184
1.3. The fundamental filtering equation 185
1.4. Dual optimal control problem 187
1.5. Particular cases 188
1.6. Dependence of the error of the optimal estimate on the delay 189
1.7. Some generalizations 195
2. Filtering of solutions of ltd equations with delay 195
2.1. Problem statement 196
2.2. Dual control problem 196
Bibliography 199
Index 233
|
| any_adam_object | 1 |
| author | Kolmanovskij, Vladimir B. Myškis, Anatolij D. 1920-2009 |
| author_GND | (DE-588)106775057 |
| author_facet | Kolmanovskij, Vladimir B. Myškis, Anatolij D. 1920-2009 |
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| ctrlnum | (OCoLC)246570416 (DE-599)BVBBV008038417 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T17:13:19Z |
| institution | BVB |
| isbn | 0792320131 |
| language | English |
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| physical | XV, 234 S. graph. Darst. |
| publishDate | 1992 |
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| publisher | Kluwer Acad. Publ. |
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| series2 | Mathematics and its applications / Soviet series |
| spelling | Kolmanovskij, Vladimir B. Verfasser aut Applied theory of functional differential equations by V. Kolmanovskii and A. Myshkis Dordrecht u.a. Kluwer Acad. Publ. 1992 XV, 234 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 85 Functional differential equations Funktional-Differentialgleichung (DE-588)4155668-9 gnd rswk-swf Funktional-Differentialgleichung (DE-588)4155668-9 s DE-604 Myškis, Anatolij D. 1920-2009 Verfasser (DE-588)106775057 aut Soviet series Mathematics and its applications 85 (DE-604)BV004708148 85 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005288581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kolmanovskij, Vladimir B. Myškis, Anatolij D. 1920-2009 Applied theory of functional differential equations Functional differential equations Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| subject_GND | (DE-588)4155668-9 |
| title | Applied theory of functional differential equations |
| title_auth | Applied theory of functional differential equations |
| title_exact_search | Applied theory of functional differential equations |
| title_full | Applied theory of functional differential equations by V. Kolmanovskii and A. Myshkis |
| title_fullStr | Applied theory of functional differential equations by V. Kolmanovskii and A. Myshkis |
| title_full_unstemmed | Applied theory of functional differential equations by V. Kolmanovskii and A. Myshkis |
| title_short | Applied theory of functional differential equations |
| title_sort | applied theory of functional differential equations |
| topic | Functional differential equations Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| topic_facet | Functional differential equations Funktional-Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005288581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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