Research on evolution equations compendium Volume 1 / Gaston M. N'Guerekata (editor).

Format:

Book

Contributor:

N'Guerekata, Gaston M., 1953-

Series:

v. 2: Evolution equations research Research on evolution equations compendium

Language:

English

Subjects (All):

Evolution equations.

Mathematics.

Physical Description:

1 online resource (438 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, 2009.

Language Note:

English

Summary:

Contains papers on the theory and methods of linear or non-linear evolutions as well as their further applications.

Contents:

Intro

RESEARCH ON EVOLUTION EQUATIONS COMPENDIUM VOLUME 1

CONTENTS

PREFACE

Chapter1DOUBLESCALECONVERGENCEANDHOMOGENIZATIONOFQUASILINEARPARABOLICEQUATIONS

Abstract

1.Introduction

2.FormulationoftheProblem

3.DoubleScaleConvergenceandtheMainTheorem

References

Chapter2SECONDGRADEFLUIDSWITHENHANCEDVISCOSITYASDYNAMICALSYSTEMS

2.SettingoftheProblem

3.ExistenceoftheGlobalAttractor

4.ExistenceofExponentialAttractors

Acknowledgments

Chapter3PERIODICSOLUTIONSOFSOMEEVOLUTIONEQUATIONSWITHINFINITEDELAY∗

2.SolutionsandTheirEstimations

3.ExistenceofPeriodicSolutions

4.AMasseraTypeTheorem

Chapter4INTERNALPOLLUTIONANDDISCRIMINATINGSENTINELINPOPULATIONDYNAMICSPROBLEM

1.1.PopulationDynamicsProblemwithMissingData

1.2.EquivalencetoNull-ControllabilitywithConstraintsontheControl

1.3.ControllabilityProblem

2.Null-ControllabilitywithConstraintsontheControl

2.1.ObservabilityInequalityAdaptedtoConstraints

2.2.ExistenceofOptimalControlVariable

3.OptimalitySystemfortheOptimalControlVariable

4.DiscriminatingSentinels

5.Conclusion

Aknowledgments

Chapter5CENTERMANIFOLDANDSTABILITYINCRITICALCASESFORSOMEPARTIALFUNCTIONALDIFFERENTIALEQUATIONS∗

2.SpectralAnalysisandVariationofConstantsFormula

3.GlobalExistenceoftheCenterManifold

4.AttractivenessoftheCenterManifold

5.FlowontheCenterManifold

6.StabilityinCriticalCases

7.LocalExistenceoftheCenterManifold

8.Application

Chapter6STABILITYRADIIOFPOSITIVELINEARFUNCTIONALDIFFERENTIALSYSTEMSINBANACHSPACES

2.Preliminaries.

3.StabilityRadiiofLinearAbstractFunctionalDifferentialEquationsunderMulti-perturbations

3.1.AbstractFunctionalDifferentialEquations

3.2.StabilityRadii

4.StabilityRadiiofPositiveLinearFunctionalDifferentialEquationsunderMulti-affinePerturbations

Chapter7EFFECTSOFNONLOCALITYANDPHASESHIFTDEFINITIONSINGENERALIZINGLEVINSON'STHEOREM

2.MethodofApproach

3.ExtensiontoNonlocalPotentials

4.PropertiesofD+(k),D(k),andL+(k)foraNonlocalPoten-tial

5.Solutionsatk=0

6.DerivationoftheGeneralizedLevinson'sTheoremforthePhaseShift

6.1.CaseofnBoundStatesandOneHalf-BoundState

6.2.CaseofnBoundStatesandmContinuumBoundStates

6.3.CaseofnBoundStatesandpSpuriousStates

6.4.Summary

7.DerivationoftheGeneralizedLevinson'sTheoremforthePhaseShift

7.1.CaseofnBoundStatesandOneHalf-BoundState

7.2.CaseofnBoundStatesandmContinuumBoundStates

7.3.CaseofnBoundStatesandpSpuriousStates

7.4.Summary

8.Examples

8.1.YamaguchiPotential

8.1.1.PhaseShiftCalculationUsingδL

8.1.2.PhaseShiftCalculationUsingδD

8.2.BeregiPotential

8.2.1.PhaseShiftCalculationUsingδL(k)

8.2.2.PhaseShiftCalculationUsingδL

9.SummaryandConclusion

Chapter8ASYMPTOTICBEHAVIOROFTHEFITZHUGH-NAGUMOSYSTEM

2.MainResults

3.ASemigroupAssociatedwithProblem(2.1)-(2.3)

4.UniformEstimatesinTime

5.ExistenceofGlobalAttractors

6.UniformBoundsofGlobalAttractorsin

7.CompactnessoftheUnionofGlobalAttractors

8.UpperSemicontinuityofGlobalAttractors

Chapter9APARTIALDIFFERENTIALEQUATIONWITHNONAUTONOMOUSPASTDELAYINL1-PHASESPACE

2.Preliminaries

3.WellposednessofPartialDifferentialEquationswithNonau-tonomousPastDelay

4.AsymptoticBehaviourofPartialDifferentialEquationswithNonautonomousPastDelay

5.Application.

5.1.ThePopulationEquationasanAbstractEquationwithNonautonomousPastDelay

5.2.WellposednessandAsymptoticBehaviorofthePopulationEquation

Chapter10SOLVINGTHEHYPERBOLICPROBLEMOBTAINEDBYTRANSMUTATIONOPERATOR

2.ExistenceoftheTransmutationOperator

3.RiemannMethod

Chapter11ELLIPTICOPERATORSWITHVARIABLECOEFFICIENTSGENERATINGFRACTIONALRESOLVENTFAMILIES

Introduction

1.PreliminariesonFractionalResolventFamilies

2.EllipticDifferentialOperatorsonL2

Chapter12EXISTENCERESULTSFORPSEUDOALMOSTPERIODICDIFFERENTIAL,FUNCTIONAL,ANDNEUTRALINTEGRALEQUATIONS

2.1.PseudoAlmostPeriodicFunctions

2.2.TheZima'sFixed-PointTheorem

3.PseudoAlmostPeriodicSolutions

3.1.PseudoAlmostPeriodicSolutionsToEq.(1.1)

3.2.PseudoAlmostPeriodicSolutionstoEq.(1.2)

4.PseudoAlmostPeriodicSolutionsToSomePartialEvolutionEquations

4.1.PseudoAlmostPeriodicSolutionstoEq.(1.3)

4.2.PseudoAlmostPeriodicSolutionstoEq.(1.4)

5.CaseoftheLogisticEquationwithDelay

Chapter13ANASYMPTOTICMODELOFANONLINEARKELVIN-VOIGTVISCOELASTICPLATE∗

2.Set-upoftheProblem

3.ScalingsofUnknowns

Chapter14MATHEMATICALANALYSISOFABILATERALOBSTACLEPROBLEMFORACLASSOFSECOND-ORDEROPERATORS

1.1.MathematicalFramework

1.2.MainNotationsandAssumptionsonData

1.3.TwoConceptsofWeakSolutions

2.TheUniquenessTheorem

3.TheViscosityandPenalizationMethods

3.1.SomeaprioriEstimates

3.2.ConvergencetowardanEntropyProcessSolution

Chapter15APPLICATIONOFTHEPICARDOPERATORSTOSECONDORDERODE'S

3.TheMainResult

4.Application

References.

Chapter16DOUBLYNONLINEARDEGENERATEPARABOLICEQUATIONSONCARNOTGROUPS∗

2.NotationandPreliminaryResult

3.NonexistenceResults

Chapter17SOMESCALARCONSERVATIONLAWSWITHDISCONTINUOUSFLUX

2.DefinitionofanEntropySolution

3.ConditionsattheInterface{x0=0}

4.TheUniquenessTheorem

5.ExistenceofanEntropySolution

5.1.FirstStep:u0∈C∞c( )

5.2.SecondStep:u0∈L∞( )

6.Generalisation

Chapter18ANEWEXACTSOLUTIONTOTHEDELAYEDDIFFUSIONEQUATION

2.MathematicalAnalysis

2.1.ProblemFormulation

2.2.DerivationofaKnownSolution

2.3.CaseofZeroDelay:DiffusionEquationSolution

3.SolutioninTermsoftheLambertW-function

3.1.TheInversionIntegral

3.2.ExactTimeDomainSolution

3.3.AnalyticalResults

4.NumericalResults

5.Summary

Chapter19LEVELSETSFORREACTIONDIFFUSIONEQUATIONS

2.TheOneDimensionalCase

3.Then-DimensionalCase

Chapter20ONTHEALMOSTPERIODICITYOFTHESUPERPOSITIONOFFUNCTIONS

3.MainResults

Acknowledgment

Chapter21TIMEPERIODICSOLUTIONSFORQUASIGEOSTROPHICMOTIONANDTHEIRSTABILITY

2.TheMainResults

3.Conclusion

Chapter 22 JACOBIAN FEEDBACK LOOPS ANALYSIS II:STABILITY AND INSTABILITY

1. Introduction

1.1. Jacobian Loops: De nitions and Notations.

2. Loops and Jacobian Spectrum

3. Loop Stability

3.1. Loop Analysis in the Plane.

3.2. Loop Analysis for 3-dimensional System.

3.3. The Lorenz System.

3.4. Rossler System.

Chapter23EXISTENCEOFOSCILLATINGSOLUTIONFORNONLINEARSTATE-DEPENDENTDELAYDIFFERENTIALEQUATION∗

2.ProofofTheorems1.1and1.2

3.ProofofTheorems1.3and1.4.

4.Examples

Chapter24SEMILINEARABSTRACTDIFFERENTIALEQUATIONSWITHDEVIATEDARGUMENT

2.BasicResults

Chapter25SINGULARSOLUTIONSOFASEMI-LINEARELLIPTICEQUATIONONNONSMOOTHDOMAINS

2.PreliminariesandKnownResults

3.ProofofTheorem1.1.

4.TheClassesKloc(D)andK(D).

Chapter26EXISTENCEOFWEIGHTEDPSEUDOALMOSTPERIODICSOLUTIONSTOSOMENON-AUTONOMOUSDIFFERENTIALEQUATIONS

3.PropertiesofWeightedPseudoAlmostPeriodicFunctions

4.WeightedPseudoAlmostPeriodicSolutions

5.Example

Chapter27AKRASNOSELSKII-TYPEFIXEDPOINTTHEOREMFORMULTIFUNCTIONSDEFINEDONAHYPERCONVEXSPACE

3.MainResult

4.Remarks

INDEX

Blank Page.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-61209-404-X

OCLC:

847446821