简介：Thenumericalmethodsformiscibledisplacmentinaggregatedorsorbingmediumareconsidered.Amixedfiniteelementmethodisadoptedforthepressureequation.Theconcentra-tioninthemobilewaterisapproximatedbyacombinationofaGalerkinfiniteelementmethodandthemethodofcharacteristicsandtheconcentrationinimmobilewaterisapproximatedbyastan-dardGalerkinmethod.Themovingmeshtechniquewhichdependsontimetisadoptedhere.Themovingmeshescanvaryindifferentspacialdomainswithdifferentvariabletimes.OptimaerrorestimatesinenergynormandL2normareobtainedundercertainconstraints.

简介：Astrongandhereditarysymmetryoperatorforamulticomponentwaterwaveequationisfoundwhichyieldsahierarchyofclassicalsymmetries.FurthermoreitisshownthatEq.(3.1)possessesnewsymmetrieswhichdependexplicitlyonthetime-variabletandallofthesymmetriesforEq.(3.1)formaninfinitelydimensionalLiealgebra.

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简介：Abstract.OnthebasisofclassificationofgeographicalpropertiesarollingdevelopmentgoalprogrammingmodelisformulatedincorrespondencewiththeecopatterngroupinFour-LakeArea.Inthismodel,thecontrolofschistosomiasisandstrengthen-Lugofthedrainage-storagefunctionarebothregardedasecologicalmeasuresduringtheprocessofmulti-year(r0)ecologicaleconomicrollingdevelopmenttomaketheecoagrlculturalsysteminthisareaintoastablyoperating,ordered,andgoodcyclicsystemunderthesupportofsomecontrollablefactors.

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简介：Inthisarticle,weconsideratwo-componentnonlinearshallowwatersystem,whichincludesthefamous2-componentCamassa-HolmandDegasperis-Procesiequationsasspecialcases.Thelocalwell-posedessforthisequationsisestablished.Somesufficientconditionsforblow-upofthesolutionsinfinitetimearegiven.Moreover,byseparationmethod,theself-similarsolutionsforthenonlinearshallowwaterequationsareobtained,andwhichlocalorglobalbehaviorcanbedeterminedbythecorrespondingEmdenequation.