简介:THEPATHWISESOLUTIONFORACLASSOFQUASILINEARSTOCHASTICDIFFERENTIALEQUATIONINBANACHSPACESIHuYaozhong(胡耀忠)(WuhanInst.ofMath.Sci.,C...
简介:OnCopositiveInthispapertheauthorwritesasimplecharacterizationforthebestcopositiveapproximationtoelementsofC(Q)byelementsoffinitedimensionalstrictChebyshevsubspacesofC(Q)inthecasewhenQisanycompactsubsetofrealnumbers.AttheendofthepapertheauthorappliesthisresultfordifferentclassesofQ.
简介:Therearethreepartsinthisarticle.InSection1,weestablishthemodelofbranchingchainwithdriftinspace-timerandomenvironment(BCDSTRE),i.e.,thecouplingofbranchingchainandrandomwalk.InSection2,weprovethatanyBCDSTREmustbeaMarkovchainintimerandomenvironmentwhenweconsiderthedistributionoftheparticlesinspaceasarandomelement.InSection3,wecalculatethefirst-ordermomentsandthesecond-ordermomentsofBCDSTRE.
简介:AnA.D.I.Galerkinschemeforthree-dimensionalnonlinearparabolicintegro-differen-tialequationisstudied.Byusingalternating-direction,thethree-dimensionalproblemisreducedtoafamilyofsinglespacevariableproblems,thecalculationissimplified;byusingalocalapproxima-tionofthecoefficientsbasedonpatchesoffiniteelements,thecoefficientmatrixisupdatedateachtimestep;byusingRitz-Volterraprojection,integrationbypartandothertechniques,theinfluencecomingfromtheintegraltermistreated;byusinginductivehypothesisreasoning,thedifficultycomingfromthenonlinearityistreated.ForbothGalerkinandA.D.I.Galerkinschemesthecon-vergencepropertiesarerigorouslydemonstrated,theoptimalH~1-normandL~2-normestimatesareobtained.