简介：Cahn-Hilliard阶段地的数字近似当模特儿因为二阶段的不可压缩的流动在这份报纸被考虑。几有效并且为联合非线性的Cahn-Hilliard阶段地的精力马厩时间discretization计划为匹配的密度盒子和变量的系统密度大小写被构造，并且被显示满足类似于连续精力法律的分离精力法律。

简介：Thepurposeofthispaperistoprovetheuniformstabilityofmultidimensionalsubsonicphasetransitionssatisfyingtheviscosity-capillaritycriterioninavanderWaalsfluid,andfurthertoestablishthelocalexistenceofphasetransitionsolutions.

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简介：Humanimmunodeficiencyvirus(HIV)hashadaninsightfulimpactaboutthestateofhealthinessofhumanimmunesystem.Duetogreatimprovementindrugtherapy,HIVinfectionshavebeenreducedby17%overthepasteightyears.IthasbeenprovedthatmosteffectivetreatmentHAART(HighlyActiveAntiRetroviralTherapy)mainlycontrolsthediseasesprogressionbutitdoesnoteradicatethediseasescompletely.ReverseTranscriptaseInhibitordrugsspeciallyassociatedwithvirusspecificCytotoxicT-Lymphocyte(CTL)thatdeclineswithdiseaseprogression.CTLresponsesagainstAIDSpathogenesiscouldbepotentialinthedynamicsofvirusreplication,recognitionandclearanceofinfectedcells.InthisresearcharticleamathematicalmodelhasbeenproposedonthebasisofCTLresponsesuppressioninthechronicphaseofinfectionduetopresenceofvirus.WealsoconsiderthegrowthoftheviruspopulationfromtheinfectedCD4~+Tcellsbuddingprocessandfromtheotherinfectedcellslikemacrophagesandthymocytes.Ouranalyticalandnumericalstudiesareconsistentwithexistingobservationsfromalliedareas.

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简介：Two-phase,immiscible,incompressibleflowinporousmediaisgovernedbyasystemofnonlinearpartialdifferentialequations.Inmostpracticalapplicationsconvectionphysicallydominatesdiffusion,andtheobjectofthispaperistodevelopafinitedifferencemethodcombinedwiththemethodofcharacteristicsandthelumpedmassmethodtotreattheparabolicequationofthedifferentialsystem.Thismethodisshownsatisfythemaximumprincipleanditserroranalysisispresented.

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简介：Inthispaperweshallgivethecharacteristicdifferencemethodsfortwophasedisplacemeatprobleminnaturallyfracturedreservoirs.Weshallprovetheexistence,uniquenessoftheapproximatesolutionandaprioridiscreteL2-errorestimates.

简介：Twophase,miscible,incompressibleflowinporousmediaisgovernedbyasystemofnonlinearpartialdifferentialequations.Manynumericalmethodshavebeengivenbydidierentauthorstothissystem,hutthesemethodsneedveryhighregularityconditions.Actualty,inmostpracticalapplicationstheseregularityconditionscouldn'tbesatisfied.Inthispaper,theproblemofdiscontinuouscoefficientswithlowerregularityconditionsisconsideredandtheerrorestimatesaredemonstrated.

简介：Thispaperconsidersaperturbedrenewalriskprocessinwhichtheinter-claimtimeshaveaphase-typedistributionunderathresholddividendstrategy.Integro-differentialequationswithcertainboundaryconditionsforthemoment-generatingfunctionandthemthmomentofthepresentvalueofalldividendsuntilruinarederived.Explicitexpressionsfortheexpectationofthepresentvalueofalldividendsuntilruinareobtainedwhentheclaimamountdistributionisfromtherationalfamily.Finally,wepresentanexample.

简介：Themiscibledisplacementofoneincompressiblefluidbyanotherinaporousmediumisconsideredinthispaper.Theconcentrationissplitinafirst-orderhyberbolicequationandahomogeneousparabolicequationwithineachlimestep.ThepressureandUsvelocityfieldiscomputedbyamixedfiniteelementmethod.Optimalorderestimatesarederivedforthenodiffusioncaseandthediffusioncase.

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简介：Tow-phaseflowmixedvariationalformulationsofevolutionfiltrationproblemswithseawaterintrusionareanalyzed.Adualmixedfractionalflowvelocity-pressuremodelisconsideredwithanair-freshwaterandafreshwater-seawatercharacterization.Foranalysisandcomputationalpurposes,spatialdecompositionsbasedonnonoverlappingmultidomains,aboveandbelowthesealevel,arevariationallyintroducedwithinternalboundaryfluxesdualizedasweaktransmissionconstraints.Further,parallelaugmentedandexactlypenalizeddualityalgorithms,andproximationsemi-implicittimemarchingschemes,areestablishedandanalyzed.

简介：Forcompressibletwo-phasedisplacementproblem,themodifiedupwindfinitedifferencefractionalstepsschemesareputforward.Sometechniques,suchascalculusofvariations,commutativelawofmultiplicationofdifferenceoperators,decompositionofhighorderdifferenceoperators,thetheoryofpriorestimatesandtechniquesareused.OptimalorderestimatesinL2normarederivedfortheerrorintheapproximatesolution.Thismethodhasalreadybeenappliedtothenumericalsimulationofseawaterintrusionandmigration-accumulationofoilresources.

简介：EQrot1nonconformingfiniteelementapproximationtoaclassofnonlineardualphaselaggingheatconductionequationsisdiscussedforsemi-discreteandfully-discreteschemes.Byuseofaspecialproperty,thatis,theconsistencyerrorofthiselementisoforderO(h2)oneorderhigherthanitsinterpolationerrorO(h),thesupercloseresultsoforderO(h2)inbrokenH1-normareobtained.Atthesametime,theglobalsuperconvergenceinbrokenH1-normisdeducedbyinterpolationpostprocessingtechnique.Moreover,theextrapolationresultwithorderO(h4)isderivedbyconstructinganewinterpolationpostprocessingoperatorandextrapolationschemebasedontheknownasymptoticexpansionformulasofEQrot1element.Finally,optimalerrorestimateisgainedforaproposedfully-discreteschemebydifferentapproachesfromthepreviousliterature.

简介：TheembeddedboundarymethodforsolvingellipticandparabolicproblemsingeometricallycomplexdomainsusingCartesianmeshesbyJohansenandColella(1998,J.Comput.Phys.147,60)hasbeenextendedforellipticandparabolicproblemswithinteriorboundariesorinterfacesofdiscontinuitiesofmaterialpropertiesorsolutions.Secondorderaccuracyisachievedinspaceandtimeforbothstationaryandmovinginterfaceproblems.Themethodisconservativeforellipticandparabolicproblemswithfixedinterfaces.Basedonthismethod,afronttrackingalgorithmfortheStefanproblemhasbeendeveloped.Theaccuracyofthemethodismeasuredthroughcomparisonwithexactsolutiontoatwo-dimensionalStefanproblem.Thealgorithmhasbeenusedforthestudyofmeltingandsolidificationproblems.