Focus on evolution equations / Gaston M. N'Guerekata, editor.

Format:

Book

Contributor:

N'Guerekata, Gaston M., 1953-

Series:

Mathematics research developments series.

Mathematics research developments

Language:

English

Subjects (All):

Evolution equations.

Physical Description:

1 online resource (222 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2012.

Language Note:

English

Summary:

This book presents high-quality research on the theory and methods of linear or nonlinear evolution equations as well as their further applications. Equations dealing with the asymptotic behavior of solutions to evolution equations are included. This book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and quasi-periodic solutions, concave Lagragian systems and integral equations.

Contents:

Intro

FOCUS ON EVOLUTION EQUATIONS

LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA

CONTENTS

PREFACE

Chapter1NONLINEARDEGENERATEPARABOLICEQUATIONSONTHEHEISENBERGGROUP

Abstract

1.Introduction

1.1.Motivationandapproaches

2.TheFiltrationEquation(0&lt

m&lt

1)

3.TheSubellipticp-Laplacian

References

Chapter2REMARKSONTHESCHR¨ODINGEREQUATION

2.BackgroundfortheSchr¨odingerEquation

3.DiffusionandFractals

3.1.ScaleRelativity

4.RemarksonaFractalSpacetime

4.1.CommentsonCantorSets

5.HydrodynamicsandtheFractalSchr¨odingerEquation

6.Recapitulation

7.Conclusions

Chapter3EXISTENCEOFp-ALMOSTAUTOMORPHICMILDSOLUTIONTOSOMEABSTRACTDIFFERENTIALEQUATIONS

2.p-AlmostAutomorphicFunctions

3.FurtherCommentsonp-AlmostAutomorphicFunctions

4.Existenceofp-almostAutomorphicMildSolutions

Chapter4LYAPUNOVFUNCTIONFORABIDIMENSIONALSYSTEM-MODELINTHEGLUCOSEHOMEOSTASYANDCLINICALINTERPRETATIONS

2.LocalStabilityoftheEquilibriumPoints

3.MainResult

4.TheAttractionBasinandtheNonexistenceofthePeriodicSolutions

5.ComparisonwithOtherModels

Chapter5INVARIANTMANIFOLDSOFFULLYNONLINEAREVOLUTIONEQUATIONS

1.IntroductionandPreliminaries

2.MainResults

2.1.TheCaseofExponetialDichotomy

2.2.TheCaseofExponetialTrichotomy

3.Applications

Chapter6GEVREYREGULARITYFORSOMEP.D.EGOVERNINGTHEMOTIONOFAMICROPOLARFLUIDINTHETHREEDIMENSIONALCASE

2.NotationsandDefinitions

3.TheGevreyclassD

4.EstimationoftheTermS0(U)intheGevreySpaces

Chapter7EXISTENCEOFGENERALIZEDSOLUTIONSFORORDINARYDIFFERENTIALEQUATIONSINBANACHSPACES

2.Strategy.

3.ProofofTheorem2

4.ProofofTheorem2(continued)

5.FurtherRemarks

Chapter8ONTHEEXISTENCEOFALMOSTPERIODIC,PERIODICANDQUASI-PERIODICSOLUTIONSOFNEUTRALDIFFERENTIALEQUATIONSWITHPIECEWISECONSTANTARGUMENTS

2.Preliminaries

2.1.Notation

2.2.SpectralTheoryofFunctions

2.3.AlmostPeriodicFunctionsandSequences

3.MainResults

3.1.TheCharacteristicEquation

3.2.CriterionofAlmostPeriodicityofaBoundedSolution

3.3.CriterionofPeriodicityofaBoundedSolution

3.4.MasseraCriterionfortheExistenceofaPeriodicSolution

3.5.CriterionforQuasiPeriodicityofaBoundedSolution

Acknowledgments

Chapter9ONTHEASYMPTOTICEQUIVALENCEOFSOLUTIONSOFTHELINEAREVOLUTIONEQUATIONS

2.TheAsymptoticEquivalenceofStronglyContinuousEvolutionaryProcesses

3.TheAsymptoticEquivalenceofLinearDifferentialEquationsinHilbertSpace

Chapter10ONSUPERPOSITIONOFALMOSTPERIODICFUNCTIONS

Acknowledgment

Chapter11RELATIVESTABILITYINCONCAVELAGRANGIANSYSTEMS

Introduction

1.AnAuxiliaryFunction

2.ALocalStudy

3.AttractivityandOptimality

Chapter12QUASISEMIGROUPSANDEVOLUTIONEQUATIONS

2.QuasisemigroupofOperators

Chapter13CONTINUATIONANDMAXIMALREGULARITYOFFRACTIONAL-ORDEREVOLUTIONARYINTEGRALEQUATION

3.ExistenceofSolution

4.ContinuationTheorem

5.MaximalRegularity

6.Examples

INDEX.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-62081-784-5

OCLC:

923666836