The Resource The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances, by Alain Haraux, Mohamed Ali Jendoubi, (electronic resource)
The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances, by Alain Haraux, Mohamed Ali Jendoubi, (electronic resource)
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The item The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances, by Alain Haraux, Mohamed Ali Jendoubi, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances, by Alain Haraux, Mohamed Ali Jendoubi, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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 gradientlike systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the socalled 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 nonlinearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the socalled LiapunovSchmidt reduction requires a rigorous exposition of SemiFredholm 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
 Language
 eng
 Edition
 1st ed. 2015.
 Extent
 XII, 142 p. 1 illus. in color.
 Contents

 1 Introduction
 2 Some basic tools
 3 Background results on Evolution Equations. 4 Uniformly damped linear semigroups. 5 Generalities on dynamical systems. 6 The linearization method. 7 Gradientlike 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
 Isbn
 9783319234076
 Label
 The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances
 Title
 The Convergence Problem for Dissipative Autonomous Systems
 Title remainder
 Classical Methods and Recent Advances
 Statement of responsibility
 by Alain Haraux, Mohamed Ali Jendoubi
 Language
 eng
 Summary
 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 gradientlike systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the socalled 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 nonlinearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the socalled LiapunovSchmidt reduction requires a rigorous exposition of SemiFredholm 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
 http://library.link/vocab/creatorName
 Haraux, Alain
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Jendoubi, Mohamed Ali.
 SpringerLink (Online service)
 Series statement
 SpringerBriefs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Dynamics
 Ergodic theory
 Functional analysis
 Operator theory
 Differential equations
 Partial differential equations
 Label
 The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances, by Alain Haraux, Mohamed Ali Jendoubi, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 1 Introduction  2 Some basic tools  3 Background results on Evolution Equations. 4 Uniformly damped linear semigroups. 5 Generalities on dynamical systems. 6 The linearization method. 7 Gradientlike 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
 Control code
 9783319234076
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 XII, 142 p. 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319234076
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319234076
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)920519614
 Label
 The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances, by Alain Haraux, Mohamed Ali Jendoubi, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 1 Introduction  2 Some basic tools  3 Background results on Evolution Equations. 4 Uniformly damped linear semigroups. 5 Generalities on dynamical systems. 6 The linearization method. 7 Gradientlike 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
 Control code
 9783319234076
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 XII, 142 p. 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319234076
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319234076
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)920519614
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/TheConvergenceProblemforDissipative/eIHsysvnBjA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/TheConvergenceProblemforDissipative/eIHsysvnBjA/">The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances, by Alain Haraux, Mohamed Ali Jendoubi, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>