Table Of ContentFields Institute Communications
VOLUME 64
The Fields Institute for Research in Mathematical Sciences
FieldsInstituteEditorialBoard:
CarlR.Riehm,ManagingEditor
EdwardBierstone,DirectoroftheInstitute
MatheusGrasselli,DeputyDirectoroftheInstitute
JamesG.Arthur,UniversityofToronto
KennethR.Davidson,UniversityofWaterloo
LisaJeffrey,UniversityofToronto
BarbaraLeeKeyfitz,OhioStateUniversity
ThomasS.Salisbury,YorkUniversity
NorikoYui,Queen’sUniversity
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Forfurthervolumes:
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John Mallet-Paret • Jianhong Wu • Yingfie Yi
Huaiping Zhu
Editors
Infinite Dimensional
Dynamical Systems
123
TheFieldsInstituteforResearch
intheMathematicalSciences
Editors
JohnMallet-Paret JianhongWu
DivisionofAppliedMathematics DepartmentofMathematicsandStatistics
BrownUniversity YorkUniversity
Providence,RI,USA Toronto,ON,Canada
YingfieYi HuaipingZhu
GeorgiaInstituteofTechnology DepartmentofMathematicsandStatistics
SchoolofMathematics YorkUniversity
Atlanta,GA,USA Toronto,ON,Canada
ISSN1069-5265 ISSN2194-1564(electronic)
ISBN978-1-4614-4522-7 ISBN978-1-4614-4523-4(eBook)
DOI10.1007/978-1-4614-4523-4
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2012948195
MathematicsSubjectClassification(2010):34-XX,35-XX,37-XX
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Preface
Inthetypicallycolorfulfallof2008,aconferenceonInfiniteDimensionalDynam-
icalSystemswasheldatYorkUniversity,TorontofromSeptember24–28.Among
the 80 participants from all over the world, 48 invited speakers presented their
work covering a wide range of topics of infinite-dimensional dynamical systems
generatedbyparabolicpartialdifferentialequations,hyperbolicpartialdifferential
equations,solitaryequations,latticedifferentialequations,delaydifferentialequa-
tions, and stochastic differentialequations. This conferencewas also dedicated to
Professor George Sell from University of Minnesota on the occasion of his 70th
birthday.
Sell obtained his PhD degree from the University of Michigan in 1962. He
joined the faculty of the School of Mathematics at the University of Minnesota
in 1964, following 2 years as a Benjamin Pierce Instructorat Harvard University.
At Minnesota, he was the cofounder of the Institute for Mathematics and Its
Applications (IMA) and the founding director of the Army High Performance
ComputingResearchCenter.HeisthefoundingeditoroftheJournalofDynamics
and DifferentialEquationsand hasbeen servingon the editorialboardsof several
v
vi Preface
otherprofessionaljournals.Sellisaworld-renownedleaderinthefieldofdynamics
of differential equations. An author of nine books and over 100 research articles,
hehasbeenanoriginatorandpioneerinmanyimportantareasinthisfield,includ-
ing nonautonomous dynamical systems, skew-product flows, invariant manifolds
theory,infinite-dimensionaldynamicalsystems,approximationdynamics,andfluid
flows.Heisarecipientofmanyhonorsandawardsincludinganhonorarydoctorate
degree from the University of St. Petersburg and an invited address at the 1982
InternationalCongressofMathematicians.
Infinite-dimensionaldynamicalsystemsaregeneratedbyevolutionaryequations
describingtheevolutionintimeofsystemswhosestatusmustbedepictedininfinite-
dimensional phase spaces. Studying the long-term behaviors of such systems
is important to our understanding of their spatiotemporal pattern formation and
global continuation, and has been among the major sources of motivation and
applications of new development in nonlinear analysis and other mathematical
theories.Theoriesofinfinite-dimensionaldynamicalsystemshavealsofoundmore
andmoreimportantapplicationsinthephysical,chemical,andlifesciences.
Each of the 48invited speakersgavea 40-minutelecture.The lecturesare col-
lectedandpublishedinthisspecialvolumeoftheFieldsInstituteCommunications
series,dedicatedtoGeorgeSell.
Providence,RI,USA JohnMallet-Paret
Toronto,ON,Canada JianhongWu
Atlanta,GA,USA YingfeiYi
Toronto,ON,Canada HuaipingZhu
Contents
Persistence of Periodic Orbits for Perturbed Dissipative
DynamicalSystems............................................................... 1
JackK.HaleandGenevie`veRaugel
SpectralTheory for ForwardNonautonomousParabolic
EquationsandApplications..................................................... 57
JanuszMierczyn´skiandWenxianShen
ADynamicalSystemsApproachtoTravelingWaveSolutions
forLiquid/VaporPhaseTransition............................................. 101
HaitaoFanandXiao-BiaoLin
InstabilityofRadially-SymmetricSpikesinSystems
withaConservedQuantity...................................................... 119
AlinPoganandArndScheel
GlobalHopfBifurcationAnalysisofaNeuronNetworkModel
withTimeDelays................................................................. 141
MichaelY.LiandJunjieWei
Instabilityof Low DensitySupersonic Wavesof aViscous
IsentropicGasFlowThroughaNozzle........................................ 169
WeishiLiuandMyunghyunOh
ASimpleProofoftheStabilityofSolitaryWaves
intheFermi-Pasta-UlamModelNeartheKdVLimit ....................... 185
A.HoffmanandC.EugeneWayne
LittlewoodProblemforaSingularSubquadraticPotential................. 193
XiongLiandYingfeiYi
SemiflowsforNeutralEquationswithState-DependentDelays............ 211
Hans-OttoWalther
vii
viii Contents
ThresholdDynamicsofScalarLinearPeriodicDelay-Differential
Equations ......................................................................... 269
YumingChenandJianhongWu
DifferentialEquationswithRandomDelay................................... 279
S.SiegmundandT.S.Doan
BeyondDiffusion:ConditionalDispersalinEcologicalModels ............ 305
ChrisCosner
GlobalAttractorofaCoupledTwo-CellBrusselatorModel................ 319
YunchengYou
Projectorson the Generalized Eigenspaces for Partial
DifferentialEquationswithTimeDelay....................................... 353
ArnautDucrot,PierreMagal,andShiguiRuan
GlobalConvergence in Monotone and Uniformly Stable
RecurrentSkew-ProductSemiflows............................................ 391
YejuanWangandXiao-QiangZhao
TheInfiniteHierarchyofElasticShellModels:SomeRecent
ResultsandaConjecture........................................................ 407
MartaLewickaandMohammadRezaPakzad
TravelingWavefrontsinLatticeDifferentialEquationswithTime
DelayandGlobalInteraction................................................... 421
ShiwangMaandXingfuZou
Bifurcation of Limit Cycles from a Non-Hamiltonian
QuadraticIntegrableSystemwithHomoclinicLoop ........................ 445
YulinZhaoandHuaipingZhu
AnomalousDiffusioninPolymers:Long-TimeBehaviour.................. 481
DmitryA.Vorotnikov
Persistence of Periodic Orbits for Perturbed
Dissipative Dynamical Systems
JackK.HaleandGenevie`veRaugel
ThispaperisdedicatedtoProfessorGeorgeSellonthe
occasionofhisseventiethbirthday.
Abstract Thispaperisdevotedtothestudyofthepersistenceofperiodicsolutions
under perturbations in dynamical systems generated by evolutionary equations,
which are not smoothing in finite time, but only asymptotically smoothing.
Assumingthattheperiodicsolutionoftheunperturbedsystemisnon-degenerate,we
wanttoprovetheexistenceanduniquenessofaperiodicsolutionfortheperturbed
equation in the neighbourhood of the unperturbed solution (with a period near
the period of the periodic solution of the unperturbed problem). We review some
methods of proofs, used in the case of systems of ordinary differential equations,
anddiscusstheirextensionstotheinfinite-dimensionalcase.
Mathematics Subject Classification (2010): Primary 35B10, 35B25, 37L50,
37L05;Secondary35Q30,35Q35
1 Introduction
Many evolutionary partial differential equations, arising in physics, chemistry or
biology, ... depend on various parameters, which are often only approximately
known.Moreover,forcomputationalreasons,agivenevolutionaryequationisoften
J.K.Hale
CenterforDynamicalSystemsandNonlinearStudies,SchoolofMathematics,
GeorgiaInstituteofTechnology,Atlanta,GA30332,USA
G.Raugel((cid:2))
CNRS,LaboratoiredeMathe´matiquesd’Orsay,UnivParis-Sud,OrsayCedexF-91405,France
e-mail:[email protected]
J.Mallet-Paretetal.(eds.),InfiniteDimensionalDynamicalSystems,FieldsInstitute 1
Communications64,DOI10.1007/978-1-4614-4523-4 1,
©SpringerScience+BusinessMediaNewYork2013
