Lectures on nonlinear evolution equations: initial value problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Birkhäuser Springer
2015
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (VIII, 306 S.) 13 illus |
| ISBN: | 9783319218731 |
| DOI: | 10.1007/978-3-319-21873-1 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804175020634669056 |
|---|---|
| adam_text | LECTURES ON NONLINEAR EVOLUTION EQUATIONS
/ RACKE, REINHARD
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
1. GLOBAL SOLUTIONS TO WAVE EQUATIONS - EXISTENCE THEOREMS
2. L^P - L^Q-DECAY ESTIMATES FOR THE LINEAR WE EQUATION
3. LINEAR SYMMETRIC HYPERBOLIC SYSTEMS
3.1 ENERGY ESTIMATES
3.2 A GLOBAL EXISTENCE THEOREM
3.3 REMARKS ON OTHER METHODS
4. SOME INEQUALITIES
5. LOCAL EXISTENCE FOR QUASILINEAR SYMMETRIC HYPERBOLIC
6. HIGH ENERGY ESTIMATES
7. WEIGHTED A PRIORI ESTIMATES
8. GLOBAL SOLUTIONS TO WAVE EQUATIONS - PROOFS
8.1 PROOF OF THEOREM 1.1
8.2 PROOF OT THEOREM 1.2
9. OTHER METHODS
10. DEVELOPMENT OF SINGULARITIES
11. MORE EVOLUTIONS EQUATIONS
11.1 EQUATIONS OF ELASITICITY
11.1.1 INITIALLY ISOTROPIC MEDIA IN R^3
11.1.2 INITIALLY CUBIC MEDIA IN R^3
11.2 HEAT EQUATIONS
11.3 EQUATIONS OF THERMOELASTICITY
11.4 SCHROEDINGER EQUATIONS
11.5 KLEIN-GORDON EQUATIONS
11.6 MAXWELL EQUATIONS
11.7 PLATE EQUATIONS
12. FURTHER ASPECTS AND QUESTIONS
13. EVOLUTION EQUATIONS IN WAVEGUIDES
13.1 NONLINEAR WAVE EQUATIONS
13.1.1 LINEAR PART
13.1.2 NONLINEAR PART
13.2. SCHROEDINGER EQUATIONS
13.3. EQUATIONS OF ELASTICITY AND MAXWELL EQUATIONS
13.4 GENERAL WAVEGUIDES
APPENDIX
A. INTERPOLATION
B. THE THEOREM OF CAUCHY-KOWALEVSKY
C. A LOCAL EXISTENCE THEOREM FOR HYPERBOLIC-PARABOLIC SYSTEMS REFERENCES
NOTATION INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
LECTURES ON NONLINEAR EVOLUTION EQUATIONS
/ RACKE, REINHARD
: 2015
ABSTRACT / INHALTSTEXT
THIS BOOK MAINLY SERVES AS AN ELEMENTARY, SELF-CONTAINED INTRODUCTION TO
SEVERAL IMPORTANT ASPECTS OF THE THEORY OF GLOBAL SOLUTIONS TO INITIAL
VALUE PROBLEMS FOR NONLINEAR EVOLUTION EQUATIONS. THE BOOK EMPLOYS THE
CLASSICAL METHOD OF CONTINUATION OF LOCAL SOLUTIONS WITH THE HELP OF A
PRIORI ESTIMATES OBTAINED FOR SMALL DATA. THE EXISTENCE AND UNIQUENESS
OF SMALL, SMOOTH SOLUTIONS THAT ARE DEFINED FOR ALL VALUES OF THE TIME
PARAMETER ARE INVESTIGATED. MOREOVER, THE ASYMPTOTIC BEHAVIOR OF THE
SOLUTIONS IS DESCRIBED AS TIME TENDS TO INFINITY. THE METHODS FOR
NONLINEAR WAVE EQUATIONS ARE DISCUSSED IN DETAIL. OTHER EXAMPLES INCLUDE
THE EQUATIONS OF ELASTICITY, HEAT EQUATIONS, THE EQUATIONS OF
THERMOELASTICITY, SCHROEDINGER EQUATIONS, KLEIN-GORDON EQUATIONS,
MAXWELL EQUATIONS AND PLATE EQUATIONS. TO EMPHASIZE THE IMPORTANCE OF
STUDYING THE CONDITIONS UNDER WHICH SMALL DATA PROBLEMS OFFER GLOBAL
SOLUTIONS, SOME BLOW-UP RESULTS ARE BRIEFLY DESCRIBED. MOREOVER, THE
PROSPECTS FOR CORRESPONDING INITIAL-BOUNDARY VALUE PROBLEMS AND FOR OPEN
QUESTIONS ARE PROVIDED. IN THIS SECOND EDITION, INITIAL-BOUNDARY VALUE
PROBLEMS IN WAVEGUIDES ARE ADDITIONALLY CONSIDERED
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Racke, Reinhard 1958- |
| author_GND | (DE-588)110907140 |
| author_facet | Racke, Reinhard 1958- |
| author_role | aut |
| author_sort | Racke, Reinhard 1958- |
| author_variant | r r rr |
| building | Verbundindex |
| bvnumber | BV042788198 |
| classification_rvk | SK 540 |
| classification_tum | MAT 000 MAT 341f MAT 359f MAT 344f |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)922009887 (DE-599)BVBBV042788198 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-21873-1 |
| edition | 2. ed. |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:09:39Z |
| institution | BVB |
| isbn | 9783319218731 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028218076 |
| oclc_num | 922009887 |
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| publisher | Birkhäuser Springer |
| record_format | marc |
| spelling | Racke, Reinhard 1958- Verfasser (DE-588)110907140 aut Lectures on nonlinear evolution equations initial value problems Reinhard Racke 2. ed. Cham [u.a.] Birkhäuser Springer 2015 1 Online-Ressource (VIII, 306 S.) 13 illus txt rdacontent c rdamedia cr rdacarrier Mathematics Differential equations, partial Partial Differential Equations Mathematik Nichtlineare Gleichung (DE-588)4455337-7 gnd rswk-swf Globale Lösung (DE-588)4264389-2 gnd rswk-swf Wurzel Mathematik (DE-588)4258245-3 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Anfangswertproblem (DE-588)4001991-3 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s Anfangswertproblem (DE-588)4001991-3 s Globale Lösung (DE-588)4264389-2 s DE-604 Wurzel Mathematik (DE-588)4258245-3 s Nichtlineare Gleichung (DE-588)4455337-7 s Erscheint auch als Druckausgabe 978-3-319-21872-4 https://doi.org/10.1007/978-3-319-21873-1 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028218076&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028218076&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Racke, Reinhard 1958- Lectures on nonlinear evolution equations initial value problems Mathematics Differential equations, partial Partial Differential Equations Mathematik Nichtlineare Gleichung (DE-588)4455337-7 gnd Globale Lösung (DE-588)4264389-2 gnd Wurzel Mathematik (DE-588)4258245-3 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Anfangswertproblem (DE-588)4001991-3 gnd |
| subject_GND | (DE-588)4455337-7 (DE-588)4264389-2 (DE-588)4258245-3 (DE-588)4221363-0 (DE-588)4001991-3 |
| title | Lectures on nonlinear evolution equations initial value problems |
| title_auth | Lectures on nonlinear evolution equations initial value problems |
| title_exact_search | Lectures on nonlinear evolution equations initial value problems |
| title_full | Lectures on nonlinear evolution equations initial value problems Reinhard Racke |
| title_fullStr | Lectures on nonlinear evolution equations initial value problems Reinhard Racke |
| title_full_unstemmed | Lectures on nonlinear evolution equations initial value problems Reinhard Racke |
| title_short | Lectures on nonlinear evolution equations |
| title_sort | lectures on nonlinear evolution equations initial value problems |
| title_sub | initial value problems |
| topic | Mathematics Differential equations, partial Partial Differential Equations Mathematik Nichtlineare Gleichung (DE-588)4455337-7 gnd Globale Lösung (DE-588)4264389-2 gnd Wurzel Mathematik (DE-588)4258245-3 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Anfangswertproblem (DE-588)4001991-3 gnd |
| topic_facet | Mathematics Differential equations, partial Partial Differential Equations Mathematik Nichtlineare Gleichung Globale Lösung Wurzel Mathematik Nichtlineare Evolutionsgleichung Anfangswertproblem |
| url | https://doi.org/10.1007/978-3-319-21873-1 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028218076&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028218076&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rackereinhard lecturesonnonlinearevolutionequationsinitialvalueproblems |