Table Of ContentTrends in Mathematics
Research Perspectives
Paula Cerejeiras, Michael Reissig,
Irene Sabadini, Joachim Toft,
Editors
Current Trends
in Analysis, its
Applications and
Computation
Proceedings of the 12th ISAAC
Congress, Aveiro, Portugal, 2019
Trends in Mathematics
Research Perspectives
Research Perspectives collects core ideas and developments discussed at con-
ferences and workshops in mathematics, as well as their increasingly important
applicationstootherfields.Thissubseries’rapidpublicationofextendedabstracts,
openproblemsandresultsofdiscussionsensuresthatreadersareattheforefrontof
currentresearchdevelopments.
Paula Cerejeiras • Michael Reissig •
Irene Sabadini • Joachim Toft
Editors
Current Trends in Analysis,
its Applications
and Computation
Proceedings of the 12th ISAAC Congress,
Aveiro, Portugal, 2019
Editors
PaulaCerejeiras MichaelReissig
DepartmentofMathematics InstitutofAppliedAnalysis
UniversityofAveiro TUBergakademieFreiberg
Aveiro,Portugal Freiberg,Germany
IreneSabadini JoachimToft
DipartimentodiMatematica DepartmentofMathematics
PolitecnicodiMilano LinnaeusUniversity
Milano,Italy Växjö,Sweden
ISSN2297-0215 ISSN2297-024X (electronic)
TrendsinMathematics
ISSN2509-7407 ISSN2509-7415 (electronic)
ResearchPerspectives
ISBN978-3-030-87501-5 ISBN978-3-030-87502-2 (eBook)
https://doi.org/10.1007/978-3-030-87502-2
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Preface
This volume contains the contributions of the participants of the 12th ISAAC
Congress which was held at the University of Aveiro, Portugal, from 29 July to
3August2019.AlthoughtheInternationalSocietyforAnalysis,itsApplicationsand
Computation(ISAAC)supportsseveralconferences,workshops,andothereventsof
scientificnature,theISAACCongressistheprincipalbi-annualeventofthesociety.
The12thISAACCongresscontinuesthissuccessfulseriesofmeetingsinitiatedin
Delaware,USA(1997),whichhavebeenheldregularlyevery2yearssince,while
rotatingamongdifferentcountriesinEurope,America,andAsia.
Withalongtraditioninjoiningresearchersformdifferentareasofanalysisand
its applications, the 12th edition had 543 registered participantsfrom 64 different
countrieswhoattended433talksspannedby23sessions,includingsessionsofthe
specialinterestgroupsof thesociety.As a noveltyandto encouragecollaboration
between differentspecial interest groups, additionaljoint sessions were organised
aroundtopicsofcommoninterest. Lastbutnotleast, therewere also nine plenary
talksgivenby
• AfonsoBandeira—CourantInstitute,NYU,USA;
• AlexanderGrigoryan—UniversitätBielefeld,Bielefeld,Germany;
• KarlheinzGroechenig—UniversitätWien,Wien,Austria;
• HåkanHedenmalm—TheRoyalInstituteofTechnology,Sweden;
• AndréNeves—UniversityofChicago,USA;
• Roman Novikov—Centrede MathématiquesAppliquées, École Polytechnique,
France;
• TohruOzawa—WasedaUniversity,Tokyo,Japan;
• SamuliSiltanen—UniversityofHelsinki,Finland;
• DurvudkhanSuragan—NazarbayevUniversity,Kazakhstan;
whichgaveabroadoverviewonrecentdevelopmentsintheirrespectiveareas.This
greatly contributedto the high scientific level of the congress, combinedwith the
warmandrelaxedatmospherewhichprevailedduringthose5days.Itisnoteworthy
to notice that many young mathematicians used the opportunity to join ISAAC
duringthistime.
v
vi Preface
As per tradition, an award was given to young scientists for their particular
achievementsin analysis, its applications and computation. For this edition, there
was a particularly strong group of outstanding candidates. In consequence, two
ISAACAwardsforyoungscientistsweregivento:
Afonso Bandeira (Courant Institute, NYU, USA). Although young, his contri-
butions range from classic analysis to applications in inverse problems, random
matrices, optimisation, and statistical physics. Among his major contributionsare
applicationsofmethodsfromanalysisto thetheoryofdatascience. Hehaspubli-
cationsintopjournalsinbothappliedandpuremathematics,statistics,information
theory,anddatascience(e.g.CommunicationsonPureandAppliedMathematics,
Applied and Computational Harmonic Analysis, and Annals of Probability). He
was awarded a Sloan Fellowship in 2018 and is currently a full professor in the
DepartmentofMathematicsatETHZurich.
FábioPusateri(UniversityofToronto,Ontario,Canada),forhiscontributionsto
thestudyofdispersiveandwaveequations,fluiddynamics,andharmonicanalysis.
Hemademajorcontributionstothestudyofthewaterwaveproblem.Inparticular,
heprovedtheexistenceofglobalsmooth,nontrivialsolutionsofgravitywaterwaves
systems in 2D, and the existence of global solutions to initial value problems for
water waves in 3D and the long-time regularity for the gravity-capillary water-
wave model in 3D. He has published in first-class journals such as Inventiones
Mathematicae, Advances in Mathematics, Memoirs of American Mathematical
Society,ActaMathematica,andAnnalesdel’InstituteHenriPoincaré.
WhiletheplenarylecturesgivenattheCongresswillappearintheindependent
volume:P.Cerejeiras,M.Reissig(Eds.)MathematicalAnalysisandApplications-
Plenary Lectures, ISAAC 2019, Aveiro, Portugal, Springer Proceedings in Mathe-
matics andStatistics, Springer,the presentvolumecontainsselected contributions
oftalksdeliveredattheCongress.Asinpreviouseditions,someofthesessionsor
interestgroupsdecidedtopublishtheirownvolumesofproceedings,independently,
and,therefore,thesecontributionsdonotappearinthepresentcollection.
Thefollowingsessionscontributedtothepresentvolume:
• S1.ApplicationsofDynamicalSystemsTheoryinBiology,organizedbyTorsten
Lindström
• S2. Complex Analysis and Partial Differential Equations, organised by Okay
Celebi,SergeiRogosin
• S3.ComplexGeometry,organisedbyAlexanderSchmitt
• S4. Complex Variables and Potential Theory, organised by Tahir Aliyev Aze-
roglu,MassimoLanzadeCristoforis,AnatolyGolberg,SergiyPlaksa
• S5. Constructive Methods in the Theory of Composite and Porous Media,
organisedbyVladimirMityushev
• S7. Function Spaces and Applications, organised by Alexandre Almeida,
AntónioCaetano,StefanSamko
• S9. Generalized Functionsand Applications,organisedby Michael Kunzinger,
MichaelOberguggenberger,StevanPilipovic´
Preface vii
• S10. Geometric & Regularity Properties of Solutions to Elliptic and Parabolic
PDEs,organisedbyPierreBousquet,LorenzoBrasco,RolandoMagnanini
• S11.GeometriesDefinedbyDifferentialForms,organisedbyMahirBilenCan,
SergeyGrigorian,SemaSalur
• S14.PartialDifferentialEquationsonCurvedSpacetimes,organisedbyAnahit
Galstyan,MakotoNakamura,KarenYagdjian
• S15. Partial Differential Equations with Nonstandard Growth, organised by
HermenegildoBorgesdeOliveira,SergeyShmarev
• S17.QuaternionicandCliffordAnalysis,organisedbySwanhildBernstein,Uwe
Kähler,IreneSabadini,FranciscusSommen
• S18.RecentProgressinEvolutionEquations,organisedbyMarcelloD’Abbicco,
MarceloRempelEbert
• S22. Wavelet theory and its Related Topics, organised by Keiko Fujita, Akira
Morimoto
Finally,wewishtothankallorganisersofallsessionsoftheCongressfortheir
work. Their efforts—such as inviting and selecting speakers, arranging their ses-
sions,andprovidingchairpersons—greatlycontributedtotherelaxed,friendly,and
scientificatmospherewhichprevailedduringtheCongress.Thesessionorganisers
were also responsible for collecting and organising the refereeing process of the
contributionsoftheirsessiontothisvolume.
UniversityofAveiro PaulaCerejeiras
Aveiro,Portugal
TUBergakademieFreiberg MichaelReissig
Freiberg,Germany
PolitecnicodiMilano IreneSabadini
Milano,Italy
LinnaeusUniversity JoachimToft
Växjö,Sweden
July2021
Contents
PartI ApplicationsofDynamicalSystemsTheoryinBiology
BifurcationAnalysisoftheToppModel....................................... 3
ValeryA.Gaiko,AlefE.Sterk,andHenkW.Broer
OptimalHarvestinginAge-andSize-StructuredPopulationModels ..... 11
N.Hritonenko,M.C.A.Leite,andY.Yatsenko
PartII ComplexAnalysisandPartialDifferentialEquations
DirichletProblemforInhomogeneousBiharmonicEquation
inCliffordAnalysis .............................................................. 21
ÜmitAksoyandA.OkayÇelebi
ANoteontheSchwarzProbleminaRingDomain.......................... 31
A.OkayÇelebiandPelinAys¸eGökgöz
OnHierarchicalModelsofElasticShallowShellswithVoids .............. 41
BakurGulua
Well-PosednessandNumericalResultsto3DPeriodicBurgers’
EquationinLebesgue-GevreyClass ........................................... 51
RidhaSelmiandAbdelkerimChaabani
BVPfortheFirstOrderEllipticSystemsinthePlane....................... 61
NinoManjavidzeandGiorgiAkhalaia
ApplicationsofZalcman’sLemmainCN ..................................... 67
P.V.Dovbush
ix
x Contents
To the Theory of One Class of Three-DimensionalIntegral
EquationwithSuper-SingularKernelsbyTubeDomain.................... 75
NusratRajabov
PartIII ComplexGeometry
PrincipalHiggsBundlesandSchottkyRepresentations..................... 89
AnaCasimiroandSusanaFerreira
OnHodgePolynomialsofSingularCharacterVarieties..................... 99
CarlosFlorentino,AzizehNozad,JaimeSilva,andAlfonsoZamora
DiagonalDoubleKodairaStructuresonFiniteGroups ..................... 111
FrancescoPolizzi
Symmetric Differentials and the Dimension of Hitchin
ComponentsforOrbi-Curves................................................... 129
FlorentSchaffhauser
PartIV ComplexVariablesandPotentialTheory
Extremal Decomposition of a Multidimensional Complex
SpacewithPolesontheBoundaryofaPolydisk ............................. 143
IrynaDenega
SomePropertiesoftheSolutionsSpaceofIrregularEllipticSystems ..... 153
GrigoriGiorgadzeandGiorgiMakatsaria
Bases in Commutative Algebras of the Second Rank
andMonogenicFunctionsRelatedtoSomeCases
ofPlaneOrthotropy.............................................................. 163
S.V.Gryshchuk
OntheBehavioratInfinityofOneClassofHomeomorphisms............. 173
RuslanSalimovandBogdanKlishchuk
DomainPerturbationfortheSolutionofaPeriodicDirichletProblem.... 181
PaoloLuzziniandPaoloMusolino
RealAnalyticityofPeriodicLayerPotentialsUponPerturbation
ofthePeriodicityParametersandoftheSupport............................ 191
PaoloLuzzini,PaoloMusolino,andRomanPukhtaievych
DirectionalDerivativesand Stolz Condition for Bicomplex
HolomorphicFunctions ......................................................... 201
LinoF.ReséndisO.,GamalielY.TéllezS.,andLuisM.TovarS.
