简介:Inthispaper,thetheoremsconcerningthesummationofFourierserieswithparameteraregivenbyusingtheLaplacetransforms.BymeansoftheknownresultofLaplacetransforms,manynew,importantproblemsofsummationofFourierserieswithparameterinmechanicscanbesolved.
简介:AnewmethodforapproximatingtheinerseLaplacetransformispresented.WefirstchangeourLaplacetransformequationintoaconvolutiontypeintegralequation,whereTikhonovregularizationtechniquesandtheFouriertransformationareeasilyapplied.WefinallyobtainaregularizedapproximationtotheinverseLaplacetransformasfinitesum
简介:§0.IntroductionLetXbearealseparableBanachspaceandX*beitsdualspace,LetB(X)betheBorelfield,i.e.,thetopologicalσ-field.Afunctionalu:X→R’iscalledaboundedsmoothfunctional,ifn∈N,f1,…,fn∈X*andφ∈Cb∞(Rn),suchthat
简介:Letfibeaboundedsmoothdomain.Inthispaper,theauthorsdefinetheBesovspacesBpa,pon,establishtheatomicdecompositionofthesespaces,andobtaintheregularityestimateoftheDirichletproblemandtheNeumannproblemfortheLaplaceoperatoronthesespaces.
简介:Thispaperdevelopsanumericalmethodtoinvertmulti-dimensionalLaplacetransforms.Byavariabletransform,Laplacetransformsareconvertedtomulti-dimensionalHansdorffmomentproblemssothatthenumericalsolutioncanbeachieved.Stabilityestimationisalsoobtained.Numericalsimulationsshowtheefficiencyandpracticalityofthemethod.
简介:设M为S^n+1中紧致极小超曲面,Mp,n-p为Sn+1的Clifford极小超曲面,若Spec(M)=Spec(Mp,n-p)在一定条件下,我们可以得出M与Mp,n-p等距同构。
简介:Basedonlinearized2-DNavier-Stokesequation,aLaplacetransform-boundaryelementcouplingmethodforviscousfluid-structureimpactanalysisisproposed.Underassumptionofincompressibilityforthefluid,thecorrespondingequivalentboundaryintegralequationintermsofthepotentialfunctionandstreamfunctionisfirstestablishedbyLamb’stransformintheLaplacetransformdomain.Itenablesustosolveim-pactwaterproblemsinfrequencydomainbytheboundaryelementmethod,inwhichtheeffectofviscousflowonthedynamicresponsecanbetakenintoaccount.Thenacompletesolutionoftheproblemunderconsider-ationintimedomainisobtainedbymeansofDurbin’sformulasforthenumericalinversionoftheLaplacetransform.Finally,apracticalexampleisgiventoconfirmthevalidityofthepresentmethod.
简介:考察了一类非线性一维p-Laplace方程正解的多解性.主要结论表明,即使非线性项在0点和无穷远处不满足通常的增长条件,该方程仍可能有两个正解.
简介:利用非线性增生映射值域的扰动定理,研究了非线性椭圆边值问题(1)在Ls(Ω)空间中解的存在性,其中max(N,2)≤p≤s<+∞.(1){-div{(C(x)+|▽u|2)p-2/2▽u}+|u|p-2u+g(x,u(x))=fa.e.x∈Ω-〈n,(C(x)+|▽u|2)p-2/2▽u〉∈βx(u(x))a.e.x∈Γ这里f∈Ls(Ω)给定,Ω()RN为有界锥形区域,n为Γ的外法向导数,g:Ω×R→R满足Caratheodory条件且对()x∈Γ,βx是正常、凸、下半连续函数ψx=ψ(x,·)的次微分,其中ψ:Γ×R→R.本文是对笔者以往一些工作的继续和补充.