Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations

476 Pages·2019·12.54 MB·english

by  Christian Constanda

Christian Constanda
Paul Harris
Editors
Integral Methods
in Science and
Engineering
Analytic Treatment
and Numerical Approximations

Christian Constanda • Paul Harris
Editors
Integral Methods in Science
and Engineering
Analytic Treatment and Numerical
Approximations
Editors
ChristianConstanda PaulHarris
DepartmentofMathematics Computing,Engineering,andMathematics
TheUniversityofTulsa UniversityofBrighton
Tulsa,OK,USA Brighton,UK
ISBN978-3-030-16076-0 ISBN978-3-030-16077-7 (eBook)
https://doi.org/10.1007/978-3-030-16077-7
MathematicsSubjectClassification:45Exx,45E10,65R20,45D05
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Preface
The international conferences on Integral Methods in Science and Engineering
(IMSE) started in 1985 at the University of Texas–Arlington and, from 1996,
continued biennially in a variety of venues around the world. These events bring
together specialists who make use of integration techniques as essential tools in
theirresearch.Thesetypesofproceduresarecharacterizedbygenerality,elegance,
and efficiency, which are essential ingredients in the work of a wide category of
practitioners.
Thetimeandplaceofthefirst14IMSEconferencesarelistedbelow:
1985,1990: UniversityofTexas–Arlington,USA
1993: TohokuUniversity,Sendai,Japan
1996: UniversityofOulu,Finland
1998: MichiganTechnologicalUniversity,Houghton,MI,USA
2000: Banff,AB,Canada(organizedbytheUniversityofAlberta,Edmon-
ton)
2002: UniversityofSaint–Étienne,France
2004: UniversityofCentralFlorida,Orlando,FL,USA
2006: NiagaraFalls,ON,Canada(organizedbytheUniversityofWaterloo)
2008: UniversityofCantabria,Santander,Spain
2010: UniversityofBrighton,UK
2012: BentoGonçalves,Brazil(organizedbytheFederalUniversityofRio
GrandedoSul)
2014: KarlsruheInstituteofTechnology,Germany
2016: UniversityofPadova,Italy
The2018event,the15thintheseries,washostedbytheUniversityofBrighton,
UK, July 16–20, gathering participants from 16 countries on 5 continents, whose
high-quality presentations consolidated the well-deserved reputation of the IMSE
conferences as a vehicle for scientists and engineers to communicate their most
recentresultsandideasandtoforgecontactsforfutureprofessionalcollaboration.
v
vi Preface
The Organizing Committee of the conference, assisted by Laura Williams and
RichardHuckofSouthwestConferences,wascomprisedof:
PaulHarris(UniversityofBrighton),Chairman
JennyVenton(UniversityofBrighton)
DmitrySavostyanov(UniversityofBrighton)
The accomplishments of the IMSE 2018 meeting were due to a large extent
to the financial support received from the School of Computing, Engineering and
Mathematics at the University of Brighton. The participants and the Organizing
Committeewishtothankthisacademicbodyforitsunderwritingofthesuccessof
theconference.
IMSE2018includedtwominisymposia:
AsymptoticAnalysis:HomogenizationandThinStructures;organizer:M.E.Pérez–
Martínez(UniversityofCantabria)
Boundary:DomainIntegralEquations;organizer:S.Mikhailov(BrunelUniversity
London)
The next IMSE conference will be held at the University of St. Petersburg,
Russia, July 13–17, 2020. Further details will be posted in due course on the
conferencewebsite.
The peer-reviewed chapters of this volume, arranged alphabetically by first
author’s name, consist of 36 papers presented in Brighton. The editors would like
tothankthereviewersfortheirvaluablehelpandthestaffatBirkhäuser–NewYork
fortheircourteousandprofessionalhandlingofthepublicationprocess.
Tulsa,OK,USA ChristianConstanda
Brighton,UK PaulHarris
January2019
The International Steering Committee of
IMSE
ChristianConstanda(TheUniversityofTulsa),Chairman
BardoE.J.Bodmann(FederalUniversityofRioGrandedoSul)
HaroldoF.deCamposVelho(INPE,SaõJosédosCampos)
PaulJ.Harris(UniversityofBrighton)
AndreasKirsch(KarlsruheInstituteofTechnology)
MirelaKohr(Babes–BolyaiUniversityofCluj–Napoca)
MassimoLanzadeCristoforis(UniversityofPadova)
SergeyMikhailov(BrunelUniversityLondon)
DorinaMitrea(UniversityofMissouri–Columbia)
MariusMitrea(UniversityofMissouri–Columbia)
DavidNatroshvili(GeorgianTechnicalUniversity)
MariaPerel(St.PetersburgStateUniversity)
MariaEugeniaPérez–Martínez(UniversityofCantabria)
OvadiaShoham(TheUniversityofTulsa)
IainW.Stewart(UniversityofDundee)
Continuing a tradition started at the preceding conference, IMSE 2018 hosted
an exhibition of digital art that consisted of five portraits of participants and a
special conference poster, executed by artist Walid Ben Medjedel using different
techniques.Theexhibitsweremuchappreciatedbytheparticipants,who,asbefore,
commentedontherelationshipbetweendigitalartandmathematics.
The portraits and the poster have been reduced to scale and reproduced on the
nextpage.
vii
viii TheInternationalSteeringCommitteeofIMSE
DigitalArtbyWalidBenMedjedel
ChristianConstanda:comics JennyVenton:watercolor
PaulHarris:caricature PaulHarris:portrait
MariusMitrea:retrovintage IMSE2018specialposter
Contents
1 Singularity Subtraction for Nonlinear Weakly Singular
IntegralEquationsoftheSecondKind .................................. 1
MarioAhues,FilomenaD.d’Almeida,RosárioFernandes,
andPauloB.Vasconcelos
2 OntheFlowofaViscoplasticFluidinaThinPeriodicDomain....... 15
MaríaAnguianoandRenataBunoiu
3 q-CalculusFormalismforNon-extensiveParticleFilter ............... 25
Amarisio S. Araújo, Helaine C. M. Furtado,
andHaroldoF.deCamposVelho
4 Two-Operator Boundary-Domain Integral Equations
forVariable-CoefficientDirichletProblemwithGeneralData........ 37
TsegayeG.Ayele
5 Two-Operator Boundary-Domain Integral Equations
forVariableCoefficientDirichletProblemin2D ....................... 53
TsegayeG.AyeleandSolomonT.Bekele
6 SolutionofaHomogeneousVersionofLoveTypeIntegral
EquationinDifferentAsymptoticRegimes.............................. 67
LaurentBaratchart,JulietteLeblond,andDmitryPonomarev
7 ASemi-analyticalSolutionforOne-DimensionalOil
DisplacementbyMiscibleGasinaHomogeneousPorous
Medium...................................................................... 81
LuanaC.M.Cantagesso,LuaraK.S.Sousa,TamiresA.Marotto,
AnnaM.Radovanovic,AdolfoPuimePires,andAlvaroM.M.Peres
8 BendingofElasticPlates:GeneralizedFourierSeriesMethod
fortheRobinProblem ..................................................... 97
ChristianConstandaandDaleDoty
ix
x Contents
9 TheAdjointSpectralGreen’sFunctionMethodAppliedto
DirectandInverseNeutralParticleSource–DetectorProblems ...... 111
JesúsP.Curbelo,OdairP.daSilva,andRicardoC.Barros
10 RelaxationofPeriodicandNonstandardGrowthIntegrals
byMeansofTwo-ScaleConvergence..................................... 123
JoelFotsoTachago,HubertNnang,andElviraZappale
11 AStiffProblem:StationaryWavesandApproximations.............. 133
DelfinaGómez,SantiagoNavazo-Esteban,
andMaría-EugeniaPérez-Martínez
12 ModellingCreepinConcreteUnderaVariableExternalLoad....... 149
LayalHakim
13 ACombinedBoundaryElementandFiniteElementModel
ofCellMotionduetoChemotaxis ........................................ 163
PaulJ.Harris
14 NumericalCalculationbyQuadruplePrecisionHigherOrder
TaylorSeriesMethodofthePythagoreanProblem
ofThreeBodies ............................................................. 173
HiroshiHirayama
15 ShapeOptimizationforInteriorNeumannandTransmission
Eigenvalues.................................................................. 185
AndreasKleefeld
16 OntheIntegro-DifferentialRadiativeConductiveTransfer
Equation:AModifiedDecompositionMethod.......................... 197
CibeleA.Ladeia,BardoE.J.Bodmann,andMarcoT.Vilhena
17 PeriodicTransmissionProblemsfortheHeatEquation ............... 211
PaoloLuzziniandPaoloMusolino
18 OnUnitedBoundary-DomainIntegro-DifferentialEquations
for Variable Coefficient Dirichlet Problem with General
Right-HandSide............................................................ 225
SergeyE.MikhailovandZenebeW.Woldemicheal
19 RescalingandTraceOperatorsinFractionalSobolevSpaces
onBoundedLipschitzDomainswithPeriodicStructure............... 237
SergeyE.Mikhailov,PaoloMusolino,andJuliaOrlik
20 DesignandPerformanceofaMultiphaseFlowManifold.............. 253
MobinaMohammadikharkeshi,AsadMolayari,RaminDabirian,
RamS.Mohan,andOvadiaShoham