第三届华东偏微分方程会议

The3rdEastChinaPartialDifferentialEquationsConferenceContemporaryPartialDifferentialEquations–FrontierandProspectProgramDepartmentofMathematics,ECNU200673—77The3rdEastChinaPartialDifferentialEquationsConferenceContemporaryPartialDifferentialEquations–FrontierandProspect:ShanghaiBaiYuLanFoundationShanghaiLeadingAcademicDisciplineEastChinaNormalUniversityCCAESSoftware(Shanghai)CO.,LTD2006.7.3-7.7A5042(34567374757677850-900900-950950-1020TeaBreak1020-11101120-12101210-14301430-15201530-16201620-1650TeaBreakTeaBreak1650-174073Jul.,MorningChairman850900OpeningCeremony900950Mechanismoftheformationofsingularitiesforquasilinearhyperbolicsystems9501020Photographtaking10201110TheheterogeneousAllen-Cahnequationinaball:solutionswithlayersandspikes11201210Theattractorsforweaklydampednon-autonomoushyperbolicequationswithanewclassofexternalforces3Jul.,AfternoonChairman14301520Multiplepositivesolutionsforaninhomogeneoussemilinearprobleminexteriordomain15301620Viscositysolutions,HJBequationsandpassportoption16201650TeaBreak16501740InhomogeneousinfinityLaplaceequations4Jul.,MorningChairman900950RuptureofthinfilmsundervanderWaalsforces9501020TeaBreak10201110HarmonicAnalysisTechniquefortheNavier-Stokesequations11201210DiffusionmodelforHIV-1infectiondynamics4Jul.,AfternoonChairman14301520ExistenceandRegularityofMultipleSolutionsforaclassof8InfinitelyDegenerateEllipticEquations15301620Theexistenceandstabilityoftravellingwavesforacompetitionmodelwithcross-diffusion15201650TeaBreak16501740Liouvilleenergyonatopologicaltwosphere5Jul.,MorningChairman900950Onsomesupercriticalproblems9501020TeaBreak102011102-Dimensional-MinkowskiproblemanditspLgeneralizations11201210OptimalconvergencerateofbinomialtreemethodsfortheAmericanoptions6Jul.,MorningChairman900950Quasi-periodicsolutionsinnonlinearSchrödingerequations9501020TeaBreak10201110OntheFucikspectrum11201210Travellingwavesofameancurvatureflowequationinperiodicmedia6Jul.,AfternoonChairman14301520Theroleofconservedquantitiesinmultiplescaleanalysis15301620Mathematicaltheoriesincomplexfluids16201650TeaBreak16501740Existenceofpositiveentiresolutionsforpoly-harmonicequationsandsystems97Jul.,MorningChairman900950Transitionsofliquidcrystalsandcriticalvaluesofelasticcoefficients9501020TeaBreak10201110Newmonotonicityformulaeforellipticandparabolicsystem11201210Parabolicvariationalinequalitiesarisingfromoptimalinvestmentandconsumption10AbstractsDiffusionmodelforHIV-1infectiondynamicsInkyungAhnKoreaUniversityAbstract:Recentinvestigations,includingtheCD4+Tcells’homingtothelymphsysteminHIVinfectionandthelocalizedbehaviorofthevirus,exhibitstheheterogeneousnatureoftheimmunecellsandvirus.ThustheapproachofusingPDEsystemsinmodellingthedynamicsoftheinteractionsbetweenimmunecellsandvirusisparticularlypertinent.Inthistalk,areaction-diffusionsystemasaspatiallynon-homogeneousmodel,isproposed,andthequalitativepropertiesofthedynamicsystemareinvestigated.Sincethepositivesteady-stateand!-limitofthePDEsystemarecloselyrelatedtostabilizingtheinfection,conditionsareprovidedfortheexistenceofastrictlypositivesolution,asteady-stateabovecertainpositivelevels,andtheexistenceofapositive!-limit.Inaddition,theL1boundsforimmunecellsandforthevirusareestimated.Apossibleroleofstemcellsstabilizingthediseaseissuggested.Viscositysolutions,HJBequationsandpassportoptionBaojunBian(JointwithYangWang)TongjiUniversityAbstract:Inthistalk,wediscusstheviscositysolutionsofakindofHamilton-Jacobi-Bellmanequations.Suchequationsarisefromthepricingproblemofpassportoption.Thepassportoptionisacalloptiononthebalanceofatradingaccountandtheoptionholderretainsthegainfromtrading,whiletheissuerisliableforthenetloss.Wederivethepricingequationusingthedynamicprogrammingprinciple.Weprovethecomparisonprinciple,uniquenessandconvexitypreservingpropertiesfortheviscositysolutions.Wealsostudythejumpdiffusionmodel,multi-assetmodelandstateconstraintboundaryvalueproblem.ExistenceandRegularityofMultipleSolutionsforaclassofInfinitelyDegenerateEllipticEquationsHuaChenWuhanUniversityAbstract:Inthistalk,weshallstudythesemilinearproblemofthesumofsquareofvectorfieldsXwithinfinitelydegeneracy,wegivesomeresultsontheDirichletproblemforsuchkindofsemilinearellipticequations.11RuptureofthinfilmsundervanderWaalsforcesKai-SengChouTheChineseUniversityofHongKongAbstract:ThethinfilmequationisafourthorderdegenerateparabolicequationderivedfromtheNavier-Stokesequationsundersomesimplifyingassumptions.WeshallshowbyanelementaryargumentathinfilmundertheinfluenceofvanderWaalsforcesdevelopsafinite-timesingularitywhenitsinitialenergyislessthansomecriticallevel.Thisisanalogoustotheqenchingpronlemforsemilinearparabolicequationsofsecondorder.MultiplePositiveSolutionsforanInhomogeneousSemilinearProbleminExteriorDomainsYinbinDengHuazhongNormalUniversityAbstract:Thistalkiscontributedtotheinhomogeneousproblem8:Δu+K(x)up+¸f(x)=0inΩ;u0inΩ;u2H1loc(Ω)\C(¯Ω);u¯¯@Ω=0u!¹0asjxj!1;whereΩ=RNn!isanexteriordomaininRN,!½RNisaboundeddomainwithsmoothboundaryandN2.¸0,¹0andp1areso