Holdings: The convergence problem for dissipative autonomous systems

The convergence problem for dissipative autonomous systems: classical methods and recent advances

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Bibliographic Details
Main Authors:	Haraux, Alain (Author), Jendoubi, Mohamed Ali (Author)
Format:	Electronic eBook
Language:	English
Published:	Cham Springer [2015]
Series:	SpringerBriefs in mathematics
Subjects:	Mathematics Dynamics Ergodic theory Functional analysis Operator theory Differential equations Partial differential equations Dynamical Systems and Ergodic Theory Partial Differential Equations Functional Analysis Operator Theory Ordinary Differential Equations Mathematik
Online Access:	BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online Ressource (XII, 142 Seiten, 1 illus. in color)
ISBN:	9783319234076
ISSN:	2191-8198
DOI:	10.1007/978-3-319-23407-6

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adam_text	THE CONVERGENCE PROBLEM FOR DISSIPATIVE AUTONOMOUS SYSTEMS / HARAUX, ALAIN : 2015 TABLE OF CONTENTS / INHALTSVERZEICHNIS 1 INTRODUCTION 2 SOME BASIC TOOLS 3 BACKGROUND RESULTS ON EVOLUTION EQUATIONS.-4 UNIFORMLY DAMPED LINEAR SEMI-GROUPS.-5 GENERALITIES ON DYNAMICAL SYSTEMS.-6 THE LINEARIZATION METHOD.-7 GRADIENT-LIKE SYSTEMS.-8 LIAPUNOV’S SECOND METHOD - INVARIANCE PRINCIPLE.-9 SOME BASIC EXAMPLES.-10 THE CONVERGENCE PROBLEM IN FINITE DIMENSIONS 11 THE INFINITE DIMENSIONAL CASE 12 VARIANTS AND ADDITIONAL RESULTS DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. THE CONVERGENCE PROBLEM FOR DISSIPATIVE AUTONOMOUS SYSTEMS / HARAUX, ALAIN : 2015 ABSTRACT / INHALTSTEXT THE BOOK INVESTIGATES CLASSICAL AND MORE RECENT METHODS OF STUDY FOR THE ASYMPTOTIC BEHAVIOR OF DISSIPATIVE CONTINUOUS DYNAMICAL SYSTEMS WITH APPLICATIONS TO ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS, THE MAIN QUESTION BEING CONVERGENCE (OR NOT) OF THE SOLUTIONS TO AN EQUILIBRIUM. AFTER REVIEWING THE BASIC CONCEPTS OF TOPOLOGICAL DYNAMICS AND THE DEFINITION OF GRADIENT-LIKE SYSTEMS ON A METRIC SPACE, THE AUTHORS PRESENT A COMPREHENSIVE EXPOSITION OF STABILITY THEORY RELYING ON THE SO-CALLED LINEARIZATION METHOD. FOR THE CONVERGENCE PROBLEM ITSELF, WHEN THE SET OF EQUILIBRIA IS INFINITE, THE ONLY GENERAL RESULTS THAT DO NOT REQUIRE VERY SPECIAL FEATURES OF THE NON-LINEARITIES ARE PRESENTLY CONSEQUENCES OF A GRADIENT INEQUALITY DISCOVERED BY S. LOJASIEWICZ. THE APPLICATION OF THIS INEQUALITY JOINTLY WITH THE SO-CALLED LIAPUNOV-SCHMIDT REDUCTION REQUIRES A RIGOROUS EXPOSITION OF SEMI-FREDHOLM OPERATOR THEORY AND THE THEORY OF REAL ANALYTIC MAPS ON INFINITE DIMENSIONAL BANACH SPACES, WHICH CANNOT BE FOUND ANYWHERE IN A READILY APPLICABLE FORM. THE APPLICATIONS COVERED IN THIS SHORT TEXT ARE THE SIMPLEST, BUT MORE COMPLICATED CASES ARE MENTIONED IN THE FINAL CHAPTER, TOGETHER WITH REFERENCES TO THE CORRESPONDING SPECIALIZED PAPERS DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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spelling	Haraux, Alain Verfasser aut The convergence problem for dissipative autonomous systems classical methods and recent advances Alain Haraux, Mohamed Ali Jendoubi Cham Springer [2015] © 2015 1 Online Ressource (XII, 142 Seiten, 1 illus. in color) txt rdacontent c rdamedia cr rdacarrier SpringerBriefs in mathematics 2191-8198 Mathematics Dynamics Ergodic theory Functional analysis Operator theory Differential equations Partial differential equations Dynamical Systems and Ergodic Theory Partial Differential Equations Functional Analysis Operator Theory Ordinary Differential Equations Mathematik Jendoubi, Mohamed Ali Verfasser (DE-588)1083804944 aut Erscheint auch als Druckausgabe 978-3-319-23406-9 https://doi.org/10.1007/978-3-319-23407-6 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632325&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=028632325&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract
spellingShingle	Haraux, Alain Jendoubi, Mohamed Ali The convergence problem for dissipative autonomous systems classical methods and recent advances Mathematics Dynamics Ergodic theory Functional analysis Operator theory Differential equations Partial differential equations Dynamical Systems and Ergodic Theory Partial Differential Equations Functional Analysis Operator Theory Ordinary Differential Equations Mathematik
title	The convergence problem for dissipative autonomous systems classical methods and recent advances
title_auth	The convergence problem for dissipative autonomous systems classical methods and recent advances
title_exact_search	The convergence problem for dissipative autonomous systems classical methods and recent advances
title_full	The convergence problem for dissipative autonomous systems classical methods and recent advances Alain Haraux, Mohamed Ali Jendoubi
title_fullStr	The convergence problem for dissipative autonomous systems classical methods and recent advances Alain Haraux, Mohamed Ali Jendoubi
title_full_unstemmed	The convergence problem for dissipative autonomous systems classical methods and recent advances Alain Haraux, Mohamed Ali Jendoubi
title_short	The convergence problem for dissipative autonomous systems
title_sort	the convergence problem for dissipative autonomous systems classical methods and recent advances
title_sub	classical methods and recent advances
topic	Mathematics Dynamics Ergodic theory Functional analysis Operator theory Differential equations Partial differential equations Dynamical Systems and Ergodic Theory Partial Differential Equations Functional Analysis Operator Theory Ordinary Differential Equations Mathematik
topic_facet	Mathematics Dynamics Ergodic theory Functional analysis Operator theory Differential equations Partial differential equations Dynamical Systems and Ergodic Theory Partial Differential Equations Functional Analysis Operator Theory Ordinary Differential Equations Mathematik
url	https://doi.org/10.1007/978-3-319-23407-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632325&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=028632325&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT harauxalain theconvergenceproblemfordissipativeautonomoussystemsclassicalmethodsandrecentadvances AT jendoubimohamedali theconvergenceproblemfordissipativeautonomoussystemsclassicalmethodsandrecentadvances

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