Availability: Lectures on nonlinear evolution equations

Lectures on nonlinear evolution equations: initial value problems

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Bibliographic Details
Main Author:	Racke, Reinhard 1958- (Author)
Format:	Electronic eBook
Language:	English
Published:	Cham [u.a.] Birkhäuser Springer 2015
Edition:	2. ed.
Subjects:	Mathematics Differential equations, partial Partial Differential Equations Mathematik Nichtlineare Gleichung Globale Lösung Wurzel > Mathematik Nichtlineare Evolutionsgleichung Anfangswertproblem
Links:	https://doi.org/10.1007/978-3-319-21873-1 https://doi.org/10.1007/978-3-319-21873-1 https://doi.org/10.1007/978-3-319-21873-1 https://doi.org/10.1007/978-3-319-21873-1 https://doi.org/10.1007/978-3-319-21873-1 https://doi.org/10.1007/978-3-319-21873-1 https://doi.org/10.1007/978-3-319-21873-1 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
Physical Description:	1 Online-Ressource (VIII, 306 S.) 13 illus
ISBN:	9783319218731
DOI:	10.1007/978-3-319-21873-1

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Record in the Search Index

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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.
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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

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