Mathematical analysis of nonlinear dynamic processes: an introduction to processes governed by partial differential equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow, Essex
Longman
1988
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman research notes in mathematics series
176 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 423 - 446 |
| Beschreibung: | 450 S. Ill. |
| ISBN: | 0470211466 0582028809 |
Internformat
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| 100 | 1 | |a Grusa, Karl-Ulrich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical analysis of nonlinear dynamic processes |b an introduction to processes governed by partial differential equations |c K.-U. Grusa |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman |c 1988 | |
| 300 | |a 450 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 176 | |
| 500 | |a Literaturverz. S. 423 - 446 | ||
| 650 | 4 | |a Dynamique différentiable | |
| 650 | 7 | |a Dynamique différentiable |2 ram | |
| 650 | 7 | |a EDP |2 inriac | |
| 650 | 7 | |a Equations aux dérivées partielles |2 ram | |
| 650 | 7 | |a Niet-lineaire dynamica |2 gtt | |
| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Théories non linéaires | |
| 650 | 7 | |a Théories non linéaires |2 ram | |
| 650 | 7 | |a cardiologie |2 inriac | |
| 650 | 7 | |a modélisation mathématique |2 inriac | |
| 650 | 7 | |a onde non linéaire |2 inriac | |
| 650 | 7 | |a processus diffusion |2 inriac | |
| 650 | 7 | |a processus non linéaire |2 inriac | |
| 650 | 7 | |a système dynamique |2 inriac | |
| 650 | 7 | |a théorie non linéaire |2 inriac | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 7 | |a économie |2 inriac | |
| 650 | 7 | |a équation diffusion |2 inriac | |
| 650 | 7 | |a équation onde |2 inriac | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Nonlinear theories | |
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Datensatz im Suchindex
| _version_ | 1804115714464808960 |
|---|---|
| adam_text | Contents
Preface
I Model building in multiconnected domains
1.1 Variational formulation of initial boundary value problems 1
1.1.1 A parabolic initial boundary value problem in a doubly
connected domain 8
1.1.2 Algorithms for solving the parabolic problem 16
1.2 Nonlinear models 19
1.2.1 Algorithms of the nonlinear parabolic problem in a two
connected domain 20
1.2.2 Existence of the nonlinear parabolic problem 23
1.2.3 Regularity of the nonlinear parabolic problem 26
1.3 Wave phenomena in two connected domains 27
1.3.1 Model of a hyperbolic initial boundary value problem 27
1.3.2 Algorithms 28
1.4 Nonlinear wave phenomena 31
1.4.1 Regularity of the nonlinear hyperbolic problem and the
unique solution 38
1.5 Modelling methods in three connected domains 42
1.5.1 Asymptotic expansion 43
1.5.2 Algorithms of the elliptic problem 51
1.6 Model building in multiconnected domains 54
1.6.1 Asymptotic expansion and algorithms 55
1.6.2 Optimal control in a multiconnected domain 60
1.6.3 Result 66
1.7 Control applied to points in R 68
1.7.1 Existence problems 68
1.7.2 Control applied to balls in R : Existence problem 72
1.7.3 Optimal rearrangement processes within the balls in P 77
1.7.4 Domain variation 80
II Global control phenomena
11.1 Minimization problems and variational inequalities 83
11.1.1 Characterization of a parabolic control process 87
11.2 Control phenomena 89
11.2.1 Modelling methods by Dirac s distribution 89
11.2.2 Approximation of the pointwise control 90
11.3 Control concentrated on one internal point 93
11.3.1 Characterization of the optimal control 95
11.3.2 Control concentrated on a finite number of internal
points 98
11.3.3 Controlled diffusion process 100
11.3.4 Solution 103
11.4 Optimal control concentrated on a finite number of
internal points 104
11.4.1 Approximation problem 104
11.4.2 Approximation process 109
11.5 Optimal cost 111
11.5.1 Redistribution processes 114
11.5.2 Optimal cost on the boundary of the domain 118
11.5.3 Evolution of the minimal cost approaching the boundary 118
11.6 Some aspects of game theory in multiconnected domains 119
11.6.1 Variational inequalities 119
11.6.2 Diffusion processes governed by differential games 123
11.6.3 Result 127
11.6.4 Innovation processes governed by differential games 128
11.6.5 Asymptotic expansion of the optimal strategy 129
11.6.6 Wave phenomena governed by differential games 131
11.6.7 Optimal strategy 133
11.7 Diffusion processes in multiconnected domains governed
by von Stackelberg strategies 134
11.7.1 Asymptotic expansion of the bilinear form 139
11.7.2 Resume 144
11.7.3 Some remarks on the movement of pedestrians along the
street and advertising 145
11.7.4 Solution of a controlled diffusion process in a multi
connected domain 148
II.8 Optimal processes in mu Unconnected regions 149
11.8.1 Optimal control process in two and three connected
domains 150
11.8.2 Optimal process in a three connected domain 151
11.8.3 Solution of the integral inequality by asymptotic
expansion 154
11.8.4 The algorithm of the asymptotic solution 160
11.8.5 Summary 163
11.8.6 Evolution of the optimal controlled diffusion process
in a three connected domain 163
III Dynamic reaction diffusion processes
111.1 Some remarks on population dynamics 166
111.1.1 On conditions of migration processes 166
111.1.2 Derivation of the equation describing randomly
migrating populations 169
111.2 Birth, death, and selection processes 175
111.2.1 A biological model 175
111.2.2 Nonlinear migration selection processes 176
111.2.3 Reduced nonlinear differential equation system 179
111.3 On travelling waves and front 181
111.3.1 Some remarks on travelling waves 181
111.3.2 Construction of a travelling front 183
111.4 Mathematical approach to synergetics 187
111.5 Systems of reaction diffusion equations 189
111.5.1 Invariant bounded regions 189
111.5.2 Asymptotic methods 194
111.5.3 Theorem 199
111.5.4 Interactive growth of two species 200
111.5.5 Modelling predator prey phenomena 201
111.5.6 Modelling competition phenomena 204
111.5.7 Limitation of the growth 205
111.6 Stability and bifurcation in certain reaction diffusion
systems 210
111.6.1 Lotka Volterra model 210
111.6.2 Interactive growth of two species 212
111.6.3 Functional matrix 215
111.6.4 Equilibrium point 217
111.6.5 Some aspects of bifurcation 219
111.6.6 Stability of bifurcating solutions 221
111.6.7 Instability and eigenvalues 223
111.6.8 Bifurcation 227
111.7 Symmetric reaction diffusion systems 228
111.7.1 Asymptotic method 229
111.7.2 Analytic solution 231
111.7.2.1 Time independent solution 236
111.7.2.2 Time dependent solution 237
111.8 A biological global model 23 9
111.9 Nonlinear model for a chemical reaction 241
IV Nonlinear wave phenomena
IV. 1 Nonlinear waves: Breaking and run up effects 254
IV.1.1 Equation of the free surface 254
IV.1.2 Analytic solution of the water surface elevation 258
IV.1.3 System of nonlinear partial differential equations 260
IV.1.4 Breaking phenomena 266
IV.1.5 Modelling by linearizing 267
IV.1.6 Two dimensional water surface elevation 268
IV.2 Modelling influence phenomena: influence models in
economics 271
IV.2.1 Crowd movements characterized by friction phenomena
and random influence impulses 271
IV.2.2 Probability distribution of the paths 276
IV.3 Prediction of certain irreversible processes 283
IV.4.1 Crowd movement described by stochastic methods 284
IV.4.2 Crowd movement and advertising pulses 289
IV.5 Nonlinear phenomena of influence 295
IV.5.1 Threshold influence 295
IV.5.2 Influence phenomena and possible behaviour of
individuals 298
IV.5.3 Behavioural features of individuals 306
IV.5.4 Nonlinear phenomena and group building processes 308
IV.5.5 Analytic solution of the Korteweg de Vries equation 311
IV.5.6 Invariants 317
IV.5.7 Application of the invariants: Advertising and group
building 319
IV.5.8 Influence potential 320
IV.5.9 Influence level 324
IV.5.10 Possible group building processes 326
IV.5.11 Variational principle 327
IV.5.12 Distribution function 330
V Dynamic stochastic models
V.1 Some remarks on stochastic modelling 333
V.1.1 Stochastic differential equations and impulse control 333
V.1.2 Model in economics 335
V.1.3 Optimal strategies 338
V.2 Some remarks on the Wiener process 339
V.2.1 Wiener integral 342
V.2.2 Infinitesimal generator 342
V.2.3 Existence of stochastic processes 343
V.2.4 Crowd movement as a dynamic stochastic process 349
V.2.5 Dynamics of Markovian motion 351
V.2.6 System of stochastic differential equations 352
V.2.7 Characterization of Markov processes 354
V.2.8 Dynamic equilibrium 358
V.2.9 System of coupled nonlinear partial differential
equations 359
V.2.10 Economic interpretation 361
V.2.11 Probability density of a Markov process 364
V.3 Feller semigroups and the uncertainty relation 365
VI Nonlinear interaction 373
VI.1.1 Polarization phenomena 375
VI.1.2 System of differential equations for interacting waves 377
VI.1.2.1 The solution 381
VI.1.3 Application in economics (analogue models) 382
VI.2 Nonlinear polarization phenomena 385
VI.2.1 Image transmission 385
VI.2.2 Solution of the nonlinear wave equation 388
VI.2.3 Image reconstruction 393
VI.2.4 Information reconstruction in multiconnected domains 395
VII Vortical processes in space
VII.1 Methods for modelling the genesis of cardiac arrhythmias 397
VI1.1.1 Review on the myocard contraction 397
VI1.1.2 Generation of a vortex ring 399
VII.1.3 Methods of model building 401
VII.1.4 The cross section as a free boundary value problem 4U2
VII.1.5 Variational principle and generation of a vortex 404
VII.1.6 A free boundary value problem 410
VII.1.7 Localizing the cross section of the vortex ring 412
VII.1.8 Vortex ring 419
Bibliography 423
Index 447
|
| any_adam_object | 1 |
| author | Grusa, Karl-Ulrich |
| author_facet | Grusa, Karl-Ulrich |
| author_role | aut |
| author_sort | Grusa, Karl-Ulrich |
| author_variant | k u g kug |
| building | Verbundindex |
| bvnumber | BV001308332 |
| callnumber-first | Q - Science |
| callnumber-label | QA374 |
| callnumber-raw | QA374 |
| callnumber-search | QA374 |
| callnumber-sort | QA 3374 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 880 SK 540 SK 810 |
| classification_tum | MAT 344f |
| ctrlnum | (OCoLC)17878666 (DE-599)BVBBV001308332 |
| dewey-full | 515.3/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/53 |
| dewey-search | 515.3/53 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV001308332 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:27:00Z |
| institution | BVB |
| isbn | 0470211466 0582028809 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000789742 |
| oclc_num | 17878666 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-384 DE-739 DE-20 DE-703 DE-355 DE-BY-UBR DE-706 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-384 DE-739 DE-20 DE-703 DE-355 DE-BY-UBR DE-706 DE-83 DE-11 DE-188 |
| physical | 450 S. Ill. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Longman |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Grusa, Karl-Ulrich Verfasser aut Mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations K.-U. Grusa 1. publ. Harlow, Essex Longman 1988 450 S. Ill. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 176 Literaturverz. S. 423 - 446 Dynamique différentiable Dynamique différentiable ram EDP inriac Equations aux dérivées partielles ram Niet-lineaire dynamica gtt Partiële differentiaalvergelijkingen gtt Théories non linéaires Théories non linéaires ram cardiologie inriac modélisation mathématique inriac onde non linéaire inriac processus diffusion inriac processus non linéaire inriac système dynamique inriac théorie non linéaire inriac Équations aux dérivées partielles économie inriac équation diffusion inriac équation onde inriac Differentiable dynamical systems Differential equations, Partial Nonlinear theories Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Dynamisches System (DE-588)4013396-5 s DE-604 Nichtlineares dynamisches System (DE-588)4126142-2 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Pitman research notes in mathematics series 176 (DE-604)BV000022845 176 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000789742&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grusa, Karl-Ulrich Mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations Pitman research notes in mathematics series Dynamique différentiable Dynamique différentiable ram EDP inriac Equations aux dérivées partielles ram Niet-lineaire dynamica gtt Partiële differentiaalvergelijkingen gtt Théories non linéaires Théories non linéaires ram cardiologie inriac modélisation mathématique inriac onde non linéaire inriac processus diffusion inriac processus non linéaire inriac système dynamique inriac théorie non linéaire inriac Équations aux dérivées partielles économie inriac équation diffusion inriac équation onde inriac Differentiable dynamical systems Differential equations, Partial Nonlinear theories Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4128900-6 (DE-588)4044779-0 (DE-588)4126142-2 (DE-588)4013396-5 |
| title | Mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations |
| title_auth | Mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations |
| title_exact_search | Mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations |
| title_full | Mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations K.-U. Grusa |
| title_fullStr | Mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations K.-U. Grusa |
| title_full_unstemmed | Mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations K.-U. Grusa |
| title_short | Mathematical analysis of nonlinear dynamic processes |
| title_sort | mathematical analysis of nonlinear dynamic processes an introduction to processes governed by partial differential equations |
| title_sub | an introduction to processes governed by partial differential equations |
| topic | Dynamique différentiable Dynamique différentiable ram EDP inriac Equations aux dérivées partielles ram Niet-lineaire dynamica gtt Partiële differentiaalvergelijkingen gtt Théories non linéaires Théories non linéaires ram cardiologie inriac modélisation mathématique inriac onde non linéaire inriac processus diffusion inriac processus non linéaire inriac système dynamique inriac théorie non linéaire inriac Équations aux dérivées partielles économie inriac équation diffusion inriac équation onde inriac Differentiable dynamical systems Differential equations, Partial Nonlinear theories Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamique différentiable EDP Equations aux dérivées partielles Niet-lineaire dynamica Partiële differentiaalvergelijkingen Théories non linéaires cardiologie modélisation mathématique onde non linéaire processus diffusion processus non linéaire système dynamique théorie non linéaire Équations aux dérivées partielles économie équation diffusion équation onde Differentiable dynamical systems Differential equations, Partial Nonlinear theories Nichtlineare partielle Differentialgleichung Partielle Differentialgleichung Nichtlineares dynamisches System Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000789742&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022845 |
| work_keys_str_mv | AT grusakarlulrich mathematicalanalysisofnonlineardynamicprocessesanintroductiontoprocessesgovernedbypartialdifferentialequations |