Singularly perturbed differential equations:
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Akademie-Verlag
1983
|
| Schriftenreihe: | Mathematical research
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 176 Seiten |
Internformat
MARC
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| 245 | 1 | 0 | |a Singularly perturbed differential equations |c by Herbert Goering ; Andreas Felgenhauer ; Gert Lube ; Hans-Görg Roos ; Tobiska Lutz |
| 264 | 1 | |a Berlin |b Akademie-Verlag |c 1983 | |
| 300 | |a 176 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical research |v 13 | |
| 650 | 4 | |a Boundary value problems |x Asymptotic theory | |
| 650 | 4 | |a Differential equations, Elliptic |x Asymptotic theory | |
| 650 | 4 | |a Differential equations, Parabolic |x Asymptotic theory | |
| 650 | 4 | |a Perturbation (Mathematics) | |
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Parabolische Differentialgleichung |0 (DE-588)4173245-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |D s |
| 689 | 0 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Parabolische Differentialgleichung |0 (DE-588)4173245-5 |D s |
| 689 | 1 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |D s |
| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Goering, Herbert |d 1925- |0 (DE-588)105274992 |4 aut | |
| 700 | 1 | |a Felgenhauer, Andreas |d 1951- |0 (DE-588)1238823351 |4 aut | |
| 700 | 1 | |a Lube, Gert |d 1951- |0 (DE-588)109799925 |4 aut | |
| 700 | 1 | |a Roos, Hans-Görg |d 1949- |0 (DE-588)108923479 |4 aut | |
| 700 | 1 | |a Tobiska, Lutz |d 1950- |0 (DE-588)109576454 |4 aut | |
| 830 | 0 | |a Mathematical research |v 13 |w (DE-604)BV000008585 |9 13 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-000125293 | ||
Datensatz im Suchindex
| _version_ | 1804114674139004928 |
|---|---|
| adam_text | CONTENTS
Notations 9
1. FOUNDATIONS 10
1.1. Asymptotic approximations and asymptotic expansions 10
1.2. Expansion operators 14
1.3. Asymptotic solutions 22
1.4. Stability of asymptotic methods 28
1.5* Significant degeneration of differential operators 31
Comments to Chapter 1 35
2. ESTIMATES OF THE SOLUTIONS 0? BLLIPTIC AND PARABOLIC
BOUNDARY VALUE PROBLEMS 37
2.1. Notations and Definitions 37
2.2. Existence and a priori estimates of classical solutions 39
2.3. A priori estimates for singularly perturbed elliptic
problems 45
2.4. A priori estimates for singularly perturbed parabolic
problems 51
2.5. Application of Banach s fixed point theorem. Estimates of the
solutions of special elliptic problems of second order 53
Comments to Chapter 2 56
3. PROPERTIES 07 SOLUTIONS 07 OLOBAL PROBLEMS TOR ELLIPTIC AND
PARABOLIC BOUNDARY TALUS PROBLEMS 57
Comments to Chapter 3 68
4. ASYMPTOTIC SOLUTIONS 07 BLLIPTIC AND PARABOLIC BOUNDARY
TALUS PROBLEMS 69
4.1. Global asymptotic solutions for equations of second order 69
4.2. Asymptotic solutions for equations of second order in the
simplest case 80
4.2.1. Uniform asymptotic solutions in the case r = F. 80
4.2.2. Uniform asymptotic solutions in the case T = C 85
4.2.3. Uniform asymptotic solutions in the case r=l^ 86
4.2.4. Remarks on multiply connected domains 89
4.3. Asymptotic solutions for equations of arbitrary order 90
4.3.1. Uniform asymptotic solutions in the case r = 17 90
4.3.2. Uniform asymptotic solutions in the case r = C 93
4.3.3. Uniform asymptotic solutions in the case P = Q 97
4.4. Tangential characteristics 99
4.4.1. The elliptic case 99
4.4.2. The parabolic case 107
4.5. Turning points 111
4.5.1. Isolated turning points 113
4.5.1.1. An inatable singular point in the case r = Ff 113
4.5.1.2. An lnstable singular point in the case psQ 117
4.5.1.3. Closed characteristics in the neighbourhood
of the boundary 122
4.5.1.4. An absolute stable singular point with r = FL 124
4.5.2. Singular lines 126
4.5.2.1. A singular line parallel to the characteristics 127
4.5.2.2. A singular line perpendicular to the
characteristics 128
4.6. Nonlinear elliptic problems of second order 135
4.6.1. Problems without boundary layers 135
4.6.2. Problems with boundary layers 137
Comments to Chapter 4 144
Appendix: Boundary layer problems 148
A 1 Ordinary boundary layers 148
1.1. Constant coefficients (1) 148
1.2. Constant coefficients (2) 149
1.3. Variable coefficients (1) 149
1.4. Variable coefficients (2) 150
A 2 Parabolic boundary layers (I) 151
2.1. The simplest case of an equation of second order 151
2.2. The simplest case of an equation of arbitrary order 152
2.3« Periodicity in an additional independent variable 15^
2.4. A more general equation of second order 155
A 3 Parabolic boundary layers (II) 156
3.1. Periodic solutions of equations of second order in
the simplest case 156
3.2. Periodic solutions for an equation of arbitrary order 158
3.3» A more general equation of second order 160
3.4. A special equation of second order 161
A 4 Parabolic boundary layers (III) 162
4.1. A degenerating equation of second order (1) 162
4.2. A degenerating equation of second order (2) 164
BIBLIOGRAPBT 165
SUBJECT IHDKX 175
|
| any_adam_object | 1 |
| author | Goering, Herbert 1925- Felgenhauer, Andreas 1951- Lube, Gert 1951- Roos, Hans-Görg 1949- Tobiska, Lutz 1950- |
| author_GND | (DE-588)105274992 (DE-588)1238823351 (DE-588)109799925 (DE-588)108923479 (DE-588)109576454 |
| author_facet | Goering, Herbert 1925- Felgenhauer, Andreas 1951- Lube, Gert 1951- Roos, Hans-Görg 1949- Tobiska, Lutz 1950- |
| author_role | aut aut aut aut aut |
| author_sort | Goering, Herbert 1925- |
| author_variant | h g hg a f af g l gl h g r hgr l t lt |
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| classification_tum | MAT 359f |
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| 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 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000211893 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:28Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000125293 |
| oclc_num | 10600457 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-634 DE-188 DE-83 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-634 DE-188 DE-83 |
| physical | 176 Seiten |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Akademie-Verlag |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Singularly perturbed differential equations by Herbert Goering ; Andreas Felgenhauer ; Gert Lube ; Hans-Görg Roos ; Tobiska Lutz Berlin Akademie-Verlag 1983 176 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical research 13 Boundary value problems Asymptotic theory Differential equations, Elliptic Asymptotic theory Differential equations, Parabolic Asymptotic theory Perturbation (Mathematics) Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Randwertproblem (DE-588)4048395-2 s DE-604 Parabolische Differentialgleichung (DE-588)4173245-5 s Elliptisches Randwertproblem (DE-588)4193399-0 s Goering, Herbert 1925- (DE-588)105274992 aut Felgenhauer, Andreas 1951- (DE-588)1238823351 aut Lube, Gert 1951- (DE-588)109799925 aut Roos, Hans-Görg 1949- (DE-588)108923479 aut Tobiska, Lutz 1950- (DE-588)109576454 aut Mathematical research 13 (DE-604)BV000008585 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000125293&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goering, Herbert 1925- Felgenhauer, Andreas 1951- Lube, Gert 1951- Roos, Hans-Görg 1949- Tobiska, Lutz 1950- Singularly perturbed differential equations Mathematical research Boundary value problems Asymptotic theory Differential equations, Elliptic Asymptotic theory Differential equations, Parabolic Asymptotic theory Perturbation (Mathematics) Elliptische Differentialgleichung (DE-588)4014485-9 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4173245-5 (DE-588)4048395-2 (DE-588)4193399-0 |
| title | Singularly perturbed differential equations |
| title_auth | Singularly perturbed differential equations |
| title_exact_search | Singularly perturbed differential equations |
| title_full | Singularly perturbed differential equations by Herbert Goering ; Andreas Felgenhauer ; Gert Lube ; Hans-Görg Roos ; Tobiska Lutz |
| title_fullStr | Singularly perturbed differential equations by Herbert Goering ; Andreas Felgenhauer ; Gert Lube ; Hans-Görg Roos ; Tobiska Lutz |
| title_full_unstemmed | Singularly perturbed differential equations by Herbert Goering ; Andreas Felgenhauer ; Gert Lube ; Hans-Görg Roos ; Tobiska Lutz |
| title_short | Singularly perturbed differential equations |
| title_sort | singularly perturbed differential equations |
| topic | Boundary value problems Asymptotic theory Differential equations, Elliptic Asymptotic theory Differential equations, Parabolic Asymptotic theory Perturbation (Mathematics) Elliptische Differentialgleichung (DE-588)4014485-9 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| topic_facet | Boundary value problems Asymptotic theory Differential equations, Elliptic Asymptotic theory Differential equations, Parabolic Asymptotic theory Perturbation (Mathematics) Elliptische Differentialgleichung Parabolische Differentialgleichung Randwertproblem Elliptisches Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000125293&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008585 |
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