Nonlinear Analysis, Geometry and Applications: Proceedings of the First NLAGA-BIRS Symposium, Dakar, Senegal, June 24–28, 2019 PDF
Preview Nonlinear Analysis, Geometry and Applications: Proceedings of the First NLAGA-BIRS Symposium, Dakar, Senegal, June 24–28, 2019
Trends in Mathematics Diaraf Seck Kinvi Kangni Philibert Nang Marie Salomon Sambou Editors Nonlinear Analysis, Geometry and Applications Proceedings of the First NLAGA-BIRS Symposium, Dakar, Senegal, June 24–28, 2019 Trends in Mathematics TrendsinMathematicsisaseriesdevotedtothepublicationofvolumesarisingfrom conferences and lecture series focusing on a particular topic from any area of mathematics.Itsaimistomakecurrentdevelopmentsavailabletothecommunityas rapidlyaspossiblewithoutcompromisetoqualityandtoarchivetheseforreference. ProposalsforvolumescanbesubmittedusingtheOnlineBookProjectSubmission Formatourwebsitewww.birkhauser-science.com. Materialsubmittedforpublicationmustbescreenedandpreparedasfollows: Allcontributionsshouldundergoareviewingprocesssimilartothatcarriedoutby journals and be checked for correct use of language which, as a rule, is English. 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Moreinformationaboutthisseriesathttp://www.springer.com/series/4961 Diaraf Seck • Kinvi Kangni • Philibert Nang • Marie Salomon Sambou Editors Nonlinear Analysis, Geometry and Applications Proceedings of the First NLAGA-BIRS Symposium, Dakar, Senegal, June 24–28, 2019 Editors DiarafSeck KinviKangni DepartmentofMathematicsofDecision DepartmentofMathematicsandComputer FASEG Science UniversityCheikhAntaDiopofDakar FelixHouphouetBoignyUniversity Dakar,Senegal Abidjan,Côted’Ivoire PhilibertNang MarieSalomonSambou MathematicsLaboratory UniversityAssaneSeckofZiguinchor EcoleNormaleSupérieuredeLibreville Ziguinchor,Senegal Libreville,Gabon ISSN2297-0215 ISSN2297-024X (electronic) TrendsinMathematics ISBN978-3-030-57335-5 ISBN978-3-030-57336-2 (eBook) https://doi.org/10.1007/978-3-030-57336-2 Mathematics Subject Classification: 49Q10, 65K10, 90C26, 90C27, 58E25, 49J15, 49J20, 34A45, 32A50,58B20,20G05,11S82,57R12,32J25,34C08,43-XX,22EXX ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG2020 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewhole orpart ofthematerial isconcerned, specifically therights oftranslation, reprinting, reuse ofillustrations, recitation, broadcasting, reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. Thisbookis published underthe imprint Birkhäuser, www.birkhauser-science.com, bythe registered companySpringerNatureSwitzerlandAG. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This volume contains the proceedingsof the first Biennial InternationalResearch Symposium of the Nonlinear Analysis, Geometry and Applications Project (NLAGA-BIRS), which was held at the Cheikh Anta Diop University, in Dakar, Senegal,onJune24–28,2019.ThesymposiumbroughttogetherAfricanexperts,as wellastheirinternationalpartners,topresentanddiscussnewmathematicalresults invariousfields. This bookgathersthe best nineteen paperspresented at this 4-daysymposium. It addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal trans- portation,controltheory,andmathematicalmodeling. The main goal of the NLAGA project is to advance and consolidate the development of nonlinear analysis, geometry, and their applications in West and CentralAfricawithafocusonsolvingreal-worldproblemssuchascoastalerosion, pollution,andurbannetworkandpopulationdynamicsproblems.(Formoredetails, pleasevisithttp://nlaga-simons.ucad.sn.) Thecontributionsinthisvolumeofferinsightintothecutting-edgeresearchand thoughtleadershipofmathematicalsciencesatbothAfricanandinternationallevels. Controllability theory, optimal mass transportation, stochastic approximation,and optimization are discussed in the first five papers. The next three papers focus on modeling and stability in ordinary differential equations. They are followed by fourpapersthatare devotedto partialdifferentialequationsandtwo thatfocuson geometricalanalysis of optimal shapes. The final five paperscover topics such as complexanalysisinseveralvariables,geometry,andrealalgebraicgeometry. The NLAGA-BIRS Symposium was supported by the NLAGA Grant funded by Simons Foundation, Senegal National Academy of Sciences and Techniques, Cheikh Anta Diop University, the African Center of Excellence in Mathematics and Computer Sciences at the Gaston Berger University (Saint Louis, Senegal), theAliouneDiopUniversityofBambey(Bambey,Senegal)aswellasCREFDES, IFACE, andFASEG (respectively,Institutes andFaculty forEconomicsand Man- agementofUCAD). v vi Preface We wish to thank all the contributors of this symposium for making it an outstandingscientificandintellectualevent.Finally,wethankdeeplyallthereferees whotooktheirvaluabletimetoreviewallthesubmittedpapers. Dakar,Senegal DiarafSeck Abidjan,Côted’Ivoire KinviKangni Libreville,Gabon PhilibertNang Ziguinchor,Sénegal MarieSalomonSambou Contents NullControllabilityofaNonlinearPopulationDynamicswithAge StructuringandSpatialDiffusion.............................................. 1 YacoubaSimporé NullControllabilityofaSystemofDegenerateNonlinearCoupled EquationsDerivedfromPopulationDynamics............................... 35 MamadouBirbaandOumarTraoré OptimalMassTransportforActivitiesLocationProblem .................. 67 MamadouKoné,BabacarMbayeNdiaye,andDiarafSeck Cut-offPhenomenonforConvergingProcessesin the Sense of α-DivergenceMeasures.......................................................... 97 B.DonBoscoDiattaandPapaNgom StochasticOptimizationin PopulationDynamics:The Case of Multi-siteFisheries............................................................... 119 SidyLyandDiarafSeck AHurwitzLikeCharacterizationofGUASPlanarSwitchedSystems .... 147 DaoudaNiangDiatta,MoussaBalde,andAminataD.T.Keita OPVVirusEvolution:AssessingtheRiskofcVDPVOutbreak............ 165 CouraBaldé,MountagaLam,andSamuelBowong AScalableEngineeringCombinationTherapiesforEvolutionary DynamicofMacrophages....................................................... 201 MoctarKande,RaphaëlM.Jungers,DiarafSeck,andMoussaBalde ExactSteadySolutionsforaFifteenVelocityModelofGas................. 231 Amahd’Almeida vii viii Contents MonotonyandComparisonPrinciple inNonAutonomousSize StructuredModels ............................................................... 263 Mamadou Lamine Diagne, Mamadou Moustapha Mbaye, andOusmaneSeydi A BoundaryValue Problemof SandTransportEquations: An ExistenceandHomogenizationResults........................................ 299 B.K.Thiam,M.A.M.T.Baldé,I.Faye,andD.Seck TheRoleoftheMeanCurvatureinaMixedHardy-SobolevTrace Inequality ......................................................................... 339 ElHadjiAbdoulayeThiam CouplingBetweenShapeGradientandTopologicalDerivativein 2DIncompressibleNavier-StokesFlows....................................... 359 AliouSeck,AlassaneSy,andDiarafSeck ShapeReconstructioninaNon-linearProblem .............................. 379 GuillaumeItbadioSadioandDiarafSeck The∂∂¯-ProblemfortheDifferentialFormswithBoundaryValue inCurrentsSenseDefinedinaContractibleCompletelyStrictly PseudoconvexDomainofaComplexManifold............................... 399 SalomonSambouandSouhaibouSambou IntroductiontotheResolutionofd(cid:2)d(cid:2)(cid:2) fortheSupercurrentsinthe Non-ArchimedeanFrame....................................................... 411 IbrahimaHamidineandSalomonSambou MinimalGraphsonThree-DimensionalWalkerManifolds................. 425 AbdoulSalamDiallo,AmethNdiaye,andAthoumaneNiang QuantitativeResultontheDeviationofaRealAlgebraicCurve fromItsVerticalTangents....................................................... 439 DaoudaNiangDiatta,SényDiatta,andMarie-FrançoiseRoy Algebraic Points of Degree at Most 2 on the Affine Curve y11 =x2(x−1)2 ................................................................. 459 ChérifMaminaColyandOumarSall Null Controllability of a Nonlinear Population Dynamics with Age Structuring and Spatial Diffusion YacoubaSimporé Abstract In this paper, we investigate the null controllability for a nonlinear populationdynamicsmodel.Thissystemissuchthatthenonlinearityisatthelevel ofbirths.Weshow,thatforacontrollocalizedinthespacevariableaswellaswith respectto the age,there is a time T dependenton the constraintson the age from whichthesystemisnullcontrollable.Wefirstestablishanobservabilityinequality usefulfortheproofofthenullcontrollabilityofanauxiliarysystem.Wealsoapply the Schauder’s fixed point in the proof of the null controllability of the nonlinear system.Forillustration,numericalsimulationsareprovided. 1 Introduction andMainsResults Inthispaper,westudythenull-controllabilityofaninfinitedimensionalnonlinear systemdescribingthedynamicsofage-structuredpopulationwithspatialposition. Lety beasolutionofthefollowingsystem: ∂y ∂y + −(cid:3)y+μy =χ v in(cid:6)×(0,A)×(0,T), (1) (cid:5) ∂t ∂a withtheinitialcondition y(x,a,0)=y (x,a)∈(cid:6)×(0,A) (2) 0 where,y isgivenin 0 K =L2(0,A;L2((cid:6))), Y.Simporé((cid:2)) LaboratoireLAMI,UniversitéOuaga1ProfesseurJosephKi-Zerbo,Ouagadougou,BurkinaFaso DeustoTech,FundaciónDeustoAvda.Universidades,Bilbao,Spain ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicense 1 toSpringerNatureSwitzerlandAG2020 D.Secketal.(eds.),NonlinearAnalysis,GeometryandApplications, TrendsinMathematics,https://doi.org/10.1007/978-3-030-57336-2_1
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