简介：Weconsideramathematicalmodelwhichdescribesacontactbetweenadeformablebodyandafoundation.ThecontactisbilateralandmodelledwithTresca’sfrictionlaw.Thegoalofthispaperistostudyanoptimalcontrolproblemwhichconsistsofleadingthestresstensorascloseaspossibletoagiventarget,byactingwithacontrolontheboundaryofthebody.Westateanoptimalcontrolproblemwhichadmitsatleastonesolution.Wealsointroducetheregularizedcontrolproblemforwhichwestudytheconvergencewhentheregularizationparametertendstozero.Finally,anoptimallyconditionisestablishedforthisproblem.

简介：Thispaperisintendedtobeafirststeptowardsthecontinuousdependenceofdynamicalcontactproblemsontheinitialdataaswellastheuniquenessofasolution.Moreover,itprovidesthebasisforaproofoftheconvergenceofpopulartimeintegrationschemesastheNewmarkmethod.WestudyafrictionlessdynamicalcontactproblembetweenbothlinearlyelasticandviscoelasticbodieswhichisformulatedviatheSignorinicontactconditions.ForviscoelasticmaterialsfulfillingtheKelvin-Voigtconstitutivelaw,wefindacharacterizationoftheclassofproblemswhichsatisfyaperturbationresultinanon-trivialmixofnormsinfunctionspace.Thischaracterizationisgivenintheformofastabilityconditiononthecontactstressesatthecontactboundaries.Furthermore,wepresentperturbationresultsfortwowell-establishedapproximationsoftheclassicalSignorinicondition:TheSignoriniconditionformulatedinvelocitiesandthemodelofnormalcompliance,bothsatisfyingevenasharperversionofourstabilitycondition.

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简介：ＡＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＮＯＮ－ＣＯＥＸＩＳＴＥＮＣＥＯＦＯＮＥＤＩＭＥＮＳＩＯＮＡＬＭＵＬＴＩＣＯＬＯＲＣＯＮＴＡＣＴＰＲＯＣＥＳＳＥＳＬＩＵＸＩＵＦＡＮＧ（刘秀芳）ＷＡＮＧＪＵＮ（王军）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...

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简介：Thispaperisconcernedwithasingularlimitfortheone-dimensionalcompressibleradiationhydrodynamicsmodel.ThesingularlimitweconsidercorrespondstothephysicalproblemoflettingtheBouguernumberinfinitewhilekeepingtheBoltzmannnumberconstant.InthecasewhenthecorrespondingEulersystemadmitsacontactdiscontinuitywave,WangandXie（2011）[12]recentlyverifiedthissingularlimitandprovedthatthesolutionofthecompressibleradiationhydrodynamicsmodelconvergestothestrongcontactdiscontinuitywaveintheL∞-normawayfromthediscontinuitylineatarateofε14,asthereciprocaloftheBouguernumbertendstozero.Inthispaper,WangandXie’sconvergencerateisimprovedtoε7/8byintroducinganewaprioriassumptionandsomerefinedenergyestimates.Moreover,itisshownthattheradiationfluxqtendstozerointheL∞-normawayfromthediscontinuityline,ataconvergencerateasthereciprocaloftheBouguernumbertendstozero.