Nonlinear wave equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Dekker
1996
|
| Schriftenreihe: | Pure and applied mathematics
194 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 276 S. |
| ISBN: | 0824793285 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010610138 | ||
| 003 | DE-604 | ||
| 005 | 19960307 | ||
| 007 | t | ||
| 008 | 960214s1996 |||| 00||| engod | ||
| 020 | |a 0824793285 |9 0-8247-9328-5 | ||
| 035 | |a (OCoLC)832503931 | ||
| 035 | |a (DE-599)BVBBV010610138 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91 |a DE-91G |a DE-355 |a DE-703 |a DE-29T |a DE-19 |a DE-634 |a DE-83 |a DE-11 |a DE-706 | ||
| 082 | 0 | |a 531.113301515355 | |
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 560 |0 (DE-625)143246: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a 83C75 |2 msc | ||
| 084 | |a 35L70 |2 msc | ||
| 084 | |a MAT 354f |2 stub | ||
| 084 | |a 58G17 |2 msc | ||
| 084 | |a MAT 357f |2 stub | ||
| 100 | 1 | |a Kichenassamy, Satyanad |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear wave equations |c Satyanad Kichenassamy |
| 264 | 1 | |a New York, NY [u.a.] |b Dekker |c 1996 | |
| 300 | |a XIII, 276 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 194 | |
| 650 | 0 | 7 | |a Nichtlineare Wellengleichung |0 (DE-588)4042104-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Wellengleichung |0 (DE-588)4042104-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Pure and applied mathematics |v 194 |w (DE-604)BV000001885 |9 194 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007078365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007078365 | ||
Datensatz im Suchindex
| _version_ | 1804125084659482624 |
|---|---|
| adam_text | Contents
Preface v
1 Linear Wave Propagation 1
1.1 The Fourier transform 2
Generalities 2
Basic properties 3
First applications 5
1.2 The Sobolev inequality 7
The standard Sobolev inequality 7
The Lorentz and conformal groups 10
A weighted Sobolev inequality 12
1.3 The initial value problem 12
Elementary criteria for well posedness 13
Non persistence results 14
Hyperbolicity 16
Representation formulae 17
1.4 Decay estimates 20
The method of stationary phase 20
Use of representation formulae 21
Use of global Sobolev inequalities 25
Complex interpolation 26
Local smoothing 27
Inhomogeneous problems 29
1.5 Propagation of singularities 30
Propagation of discontinuities 31
Propagation of high frequency oscillations 33
Propagation of C°° singularities 33
1.6 What is a wave? 35
1.7 Further results and problems 37
Notes 40
References 42
ix
x Contents
2 Local and Global Existence 47
2.1 The analytic Cauchy problem 49
An example 49
Method of majorants 50
Fuchsian equations 51
Basic existence theorem 52
2.2 The energy method 58
Symmetric hyperbolic systems 58
Examples 61
Leray systems 62
2.3 Semi group techniques 64
The Hille Yosida theorem 64
Application 66
Nonlinear scattering 67
2.4 Global existence for small data 69
Basic issues 69
Compactification of Minkowski space 70
Transformation formulae 72
Other approaches 75
2.5 Other iteration techniques 75
Nonlinear Klein Gordon equation 76
Finite propagation of support 77
Perturbations of the wave equation 77
2.6 Further results and problems 78
Notes 80
References 82
3 Singularity Formation 87
3.1 Criteria for breakdown 89
Scalar equations 89
Quasilinear systems 92
Blow up via differential inequalities 93
Other methods 94
3.2 Propagation of weak singularities 99
Dyadic decomposition and paraproduct 100
Action of nonlinear functions 100
Application to nonlinear equations 101
3.3 Shock waves 103
Definitions 104
Jump discontinuities 105
General form of the entropy condition 107
Single conservation law 107
3.4 Models for singularity formation 108
Contents xi
The breakdown time 109
The blow up surface: semi linear case 112
The blow up surface: quasi linear case 117
3.5 Appendix 119
Integral invariants for first order ODEs 119
The single first order equation 121
3.6 Further results and problems 124
Notes 126
References 128
4 Solitons and Inverse Scattering 135
4.1 Universal equations 137
Nearly monochromatic wavetrains 138
Long waves 140
Three wave interaction 141
Instabilities 142
4.2 Isospectrality 143
4.3 The Korteweg deVries equation 145
Eigenfunctions of L 146
Scattering data 149
Fourier transform of eigenfunctions 150
Reconstruction procedure 151
Application to the KdV equation 153
Multi solitons 154
4.4 The AKNS systems . 155
4.5 Riemann Hilbert and d formulations 160
Case of the AKNS systems 160
Generalized AKNS systems 161
Notions on the Cauchy integral and the B problem 164
4.6 Criteria for integrability 165
The WTC test 166
The symmetry test 173
Analytic characterizations 173
Hirota s method 177
Defining integrability 178
4.7 Further results and problems 179
Notes 183
References 184
5 Perturbation Methods 189
5.1 Perturbation of spectra 190
A possible pathology 190
Type (A) methods 191
xii Contents
Bounds on the number of eigenvalues 192
5.2 Implicit function theorems 192
Nash Moser theorem without smoothing 193
Nash Moser theorem with smoothing 195
An application 198
Nash Moser theorem and paradifferential operators 201
5.3 Nonlinear geometrical optics 202
5.4 Whitham s theory 204
5.5 Soliton perturbation 206
Case of the 2 x 2 AKNS system 206
CaseofKdV 208
5.6 Application of invariant manifold theory 209
Abstract results 209
Examples 210
5.7 Further results and problems 211
Notes 215
References 217
6 General Relativity 219
6.1 Preliminaries 220
Metric and connection 220
6.2 Einstein s equations 230
6.3 The Cauchy problem 236
Preliminary remarks 236
Analytic Cauchy problem 237
Non analytic Cauchy problem 238
Constraint equations 240
Characteristic initial value problem 242
6.4 Linearization stability and perturbations 243
Linearization stability 243
Other perturbation problems 245
6.5 Singularities and cosmic censorship 247
What is a singularity? 248
Singularities and horizons 249
Singularity theorems 251
6.6 Exact solutions 252
Spacetime symmetries 252
Important exact solutions 253
6.7 Further results and problems 259
Notes 265
References 267
Contents xiii
Index of Notation 273
Index 275
|
| any_adam_object | 1 |
| author | Kichenassamy, Satyanad |
| author_facet | Kichenassamy, Satyanad |
| author_role | aut |
| author_sort | Kichenassamy, Satyanad |
| author_variant | s k sk |
| building | Verbundindex |
| bvnumber | BV010610138 |
| classification_rvk | SK 540 SK 560 SK 950 |
| classification_tum | MAT 354f MAT 357f |
| ctrlnum | (OCoLC)832503931 (DE-599)BVBBV010610138 |
| dewey-full | 531.113301515355 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.113301515355 |
| dewey-search | 531.113301515355 |
| dewey-sort | 3531.113301515355 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01619nam a2200433 cb4500</leader><controlfield tag="001">BV010610138</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19960307 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960214s1996 |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0824793285</subfield><subfield code="9">0-8247-9328-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)832503931</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010610138</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">531.113301515355</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 560</subfield><subfield code="0">(DE-625)143246:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">83C75</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">35L70</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 354f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">58G17</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 357f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kichenassamy, Satyanad</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlinear wave equations</subfield><subfield code="c">Satyanad Kichenassamy</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY [u.a.]</subfield><subfield code="b">Dekker</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 276 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Pure and applied mathematics</subfield><subfield code="v">194</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Wellengleichung</subfield><subfield code="0">(DE-588)4042104-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare Wellengleichung</subfield><subfield code="0">(DE-588)4042104-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Pure and applied mathematics</subfield><subfield code="v">194</subfield><subfield code="w">(DE-604)BV000001885</subfield><subfield code="9">194</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007078365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007078365</subfield></datafield></record></collection> |
| id | DE-604.BV010610138 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:55:56Z |
| institution | BVB |
| isbn | 0824793285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007078365 |
| oclc_num | 832503931 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 DE-29T DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-706 |
| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 DE-29T DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-706 |
| physical | XIII, 276 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Kichenassamy, Satyanad Verfasser aut Nonlinear wave equations Satyanad Kichenassamy New York, NY [u.a.] Dekker 1996 XIII, 276 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 194 Nichtlineare Wellengleichung (DE-588)4042104-1 gnd rswk-swf Nichtlineare Wellengleichung (DE-588)4042104-1 s DE-604 Pure and applied mathematics 194 (DE-604)BV000001885 194 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007078365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kichenassamy, Satyanad Nonlinear wave equations Pure and applied mathematics Nichtlineare Wellengleichung (DE-588)4042104-1 gnd |
| subject_GND | (DE-588)4042104-1 |
| title | Nonlinear wave equations |
| title_auth | Nonlinear wave equations |
| title_exact_search | Nonlinear wave equations |
| title_full | Nonlinear wave equations Satyanad Kichenassamy |
| title_fullStr | Nonlinear wave equations Satyanad Kichenassamy |
| title_full_unstemmed | Nonlinear wave equations Satyanad Kichenassamy |
| title_short | Nonlinear wave equations |
| title_sort | nonlinear wave equations |
| topic | Nichtlineare Wellengleichung (DE-588)4042104-1 gnd |
| topic_facet | Nichtlineare Wellengleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007078365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT kichenassamysatyanad nonlinearwaveequations |