Traveling wave solutions of parabolic systems:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1994
|
| Schriftenreihe: | Translations of mathematical monographs
140 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XII, 448 S. graph. Darst. |
| ISBN: | 0821846094 |
Internformat
MARC
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| 100 | 1 | |a Vo'lpert, Ajzik I. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Beguščie volny opisyvaemye paraboličeskimi sistemami |
| 245 | 1 | 0 | |a Traveling wave solutions of parabolic systems |c Aizik I. Volpert ; Vitaly A. Volpert ; Vladimir A. Volpert |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1994 | |
| 300 | |a XII, 448 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 140 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Cinétique chimique - Modèles mathématiques | |
| 650 | 7 | |a Cinétique chimique - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Equations différentielles non linéaires |2 ram | |
| 650 | 7 | |a Equations différentielles paraboliques |2 ram | |
| 650 | 7 | |a Parabolische differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Reactiekinetiek |2 gtt | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Équations différentielles non linéaires | |
| 650 | 4 | |a Équations différentielles paraboliques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Chemical kinetics |x Mathematical models | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Differential equations, Parabolic | |
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| 700 | 1 | |a Vol'pert, Vladimir A. |e Verfasser |4 aut | |
| 830 | 0 | |a Translations of mathematical monographs |v 140 |w (DE-604)BV000002394 |9 140 | |
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Datensatz im Suchindex
| _version_ | 1804124316583854080 |
|---|---|
| adam_text | Contents
Preface xi
Introduction. Traveling Waves Described by Parabolic Systems 1
§ 1. Classification of waves 2
§2. Existence of waves 12
§3. Stability of waves 16
§4. Wave propagation speed 21
§5. Bifurcations of waves 23
§6. Traveling waves in physics, chemistry, and biology 31
Part I. Stationary Waves 37
Chapter 1. Scalar Equation 39
§1. Introduction 39
§2. Functionals a t and a * 45
§3. Waves and systems of waves 52
§4. Properties of solutions of parabolic equations 72
§5. Approach to waves and systems of waves 85
§6. Supplement (Additions and bibliographic commentaries) 110
Chapter 2. Leray Schauder Degree 121
§1. Introduction. Formulation of results 121
§2. Estimate of linear operators from below 128
§3. Functional c(u) and operator A{u) 134
§4. Leray Schauder degree 138
§5. Linearized operator 140
§6. Index of a stationary point 144
§7. Supplement. Leray Schauder degree in the multidimensional .
case 148
Chapter 3. Existence of Waves 151
§1. Introduction. Formulation of results 151
§2. A priori estimates 157
§3. Existence of monotone waves 171
§4. Monotone systems 174
§5. Supplement and bibliographic commentaries 180
Chapter 4. Structure of the Spectrum 183
§1. Elliptic problems with a parameter 185
§2. Continuous spectrum 188
§3. Structure of the spectrum 194
vii
viii CONTENTS
§4. Examples 204
§5. Spectrum of monotone systems 208
Chapter 5. Stability and Approach to a Wave 213
fjl. Stability with shift and its connection with the spectrum 214
§2. Stability of planar waves to spatial perturbations 221
§3. Conditions of instability 232
§4. Stability of waves for monotone systems 233
§5. On the solutions of nonstationary problems 237
§6. Approach to a monotone wave 245
§7. Minimax representation of the speed 250
Part II. Bifurcation of Waves 253
Chapter 6. Bifurcation of Nonstationary Modes of Wave Propagation 255
§ 1. Statement of the problem 255
§2. Representation of solutions in series form. Stability of
solutions 259
§3. Examples 264
Chapter 7. Mathematical Proofs 269
§ 1. Statement of the problem and linear analysis 269
§2. General representation of solutions of the nonlinear problem.
Existence of solutions 281
§3. Stability of branching off solutions 291
Part III. Waves in Chemical Kinetics and Combustion 293
Chapter 8. Waves in Chemical Kinetics 295
§ 1. Equations of chemical kinetics 295
§2. Monotone systems 302
§3. Existence and stability of waves 308
§4. Branching chain reactions 312
§5. Other model systems 328
Bibliographic commentaries 330
Chapter 9. Combustion Waves with Complex Kinetics 333
§1. Introduction 333
§2. Existence of waves for kinetic systems with irreversible
reactions 334
p. Stability of a wave in the case of equality of transport
coefficients 358
§4. Examples 362
Bibliographic commentaries 371
Chapter 10. Estimates and Asymptotics of the Speed of Combustion
Waves 373
§ 1. Estimates for the speed of a combustion wave in a condensed
medium 373
§2. Estimates for the speed of a gas combustion wave 389
§3. Determination of asymptotics of the speed by the method of
successive approximations 396
Bibliographic commentaries 405
CONTENTS ix
Supplement. Asymptotic and Approximate Analytical Methods in
Combustion Problems 407
§1. Narrow reaction zone method. Speed of a stationary
combustion wave 407
§2. Stability of a stationary combustion wave 411
§3. Nonadiabatic combustion 412
§4. Stage combustion 414
§5. Transformations in a combustion wave 419
§6. Application of the methods of bifurcation theory to the study
of nonstationary modes of propagation of combustion waves 422
§7. Surveys and monographs 426
Bibliography 427
(
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:43:44Z |
| institution | BVB |
| isbn | 0821846094 |
| language | English |
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| physical | XII, 448 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Vo'lpert, Ajzik I. Verfasser aut Beguščie volny opisyvaemye paraboličeskimi sistemami Traveling wave solutions of parabolic systems Aizik I. Volpert ; Vitaly A. Volpert ; Vladimir A. Volpert Providence, RI American Math. Soc. 1994 XII, 448 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 140 Aus dem Russ. übers. Cinétique chimique - Modèles mathématiques Cinétique chimique - Modèles mathématiques ram Equations différentielles non linéaires ram Equations différentielles paraboliques ram Parabolische differentiaalvergelijkingen gtt Reactiekinetiek gtt Wiskundige modellen gtt Équations différentielles non linéaires Équations différentielles paraboliques Mathematisches Modell Chemical kinetics Mathematical models Differential equations, Nonlinear Differential equations, Parabolic Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd rswk-swf Wanderwelle (DE-588)4189075-9 gnd rswk-swf Wanderwelle (DE-588)4189075-9 s Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 s DE-604 Volpert, Vitaly 1958- Verfasser (DE-588)144027313 aut Vol'pert, Vladimir A. Verfasser aut Translations of mathematical monographs 140 (DE-604)BV000002394 140 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006590966&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vo'lpert, Ajzik I. Volpert, Vitaly 1958- Vol'pert, Vladimir A. Traveling wave solutions of parabolic systems Translations of mathematical monographs Cinétique chimique - Modèles mathématiques Cinétique chimique - Modèles mathématiques ram Equations différentielles non linéaires ram Equations différentielles paraboliques ram Parabolische differentiaalvergelijkingen gtt Reactiekinetiek gtt Wiskundige modellen gtt Équations différentielles non linéaires Équations différentielles paraboliques Mathematisches Modell Chemical kinetics Mathematical models Differential equations, Nonlinear Differential equations, Parabolic Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd Wanderwelle (DE-588)4189075-9 gnd |
| subject_GND | (DE-588)4455524-6 (DE-588)4189075-9 |
| title | Traveling wave solutions of parabolic systems |
| title_alt | Beguščie volny opisyvaemye paraboličeskimi sistemami |
| title_auth | Traveling wave solutions of parabolic systems |
| title_exact_search | Traveling wave solutions of parabolic systems |
| title_full | Traveling wave solutions of parabolic systems Aizik I. Volpert ; Vitaly A. Volpert ; Vladimir A. Volpert |
| title_fullStr | Traveling wave solutions of parabolic systems Aizik I. Volpert ; Vitaly A. Volpert ; Vladimir A. Volpert |
| title_full_unstemmed | Traveling wave solutions of parabolic systems Aizik I. Volpert ; Vitaly A. Volpert ; Vladimir A. Volpert |
| title_short | Traveling wave solutions of parabolic systems |
| title_sort | traveling wave solutions of parabolic systems |
| topic | Cinétique chimique - Modèles mathématiques Cinétique chimique - Modèles mathématiques ram Equations différentielles non linéaires ram Equations différentielles paraboliques ram Parabolische differentiaalvergelijkingen gtt Reactiekinetiek gtt Wiskundige modellen gtt Équations différentielles non linéaires Équations différentielles paraboliques Mathematisches Modell Chemical kinetics Mathematical models Differential equations, Nonlinear Differential equations, Parabolic Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd Wanderwelle (DE-588)4189075-9 gnd |
| topic_facet | Cinétique chimique - Modèles mathématiques Equations différentielles non linéaires Equations différentielles paraboliques Parabolische differentiaalvergelijkingen Reactiekinetiek Wiskundige modellen Équations différentielles non linéaires Équations différentielles paraboliques Mathematisches Modell Chemical kinetics Mathematical models Differential equations, Nonlinear Differential equations, Parabolic Nichtlineare parabolische Differentialgleichung Wanderwelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006590966&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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