简介：1.IntroductionLetnCRN,N23,beasmoothboundeddomainandconsiderthesemilinearellipticequationswhereatbELoc(Q),AERIisaparameter.Itisasimplifiedmodelforsomeproblemsinpopulationdynamicsandinreaction-diffusionprocessess(seethereferencesof[1]).Bytheresultsof[...

简介：Byconsideringthepropertiesoff(t,u,v)/u+v,g(t,u,v)/u+v,weshovthemultiplicityofatleasttwopositivesolutionsoftheellipticsystem.

简介：Anewapproachisgiventoanalysetheregularityofsolutionsnearsingularpointsfortheinterfaceproblemsofsecondorderellipticpartialdifferentialequations.Forgeneralequationswithnonsyrnmetricdominanttermsanddiscontinuouspiecewiaesmoothcoefficients,itisprovedthatsolutionsinH^1canbedocomposedintotwoparts,oneofwhichisafinitesumofparticularsolutionstothecorrespondinghomogeneonsequationswithpiecewiseconstantcoettioionts,andtheotheroneofwhichistheregularpart.Moreoveraprioriestimationsareproven.

简介：ABSTRACT:Westudytheevolutionofsingleellipticvortexringforinitialaspectratio(AR)=2,4,6.TheincompressibleNavier-Stokesequationsaresolvedbyadealiasedpseudo-spectralmethodwith64~3gridpointsinaperiodiccube.WefindthattherearethreekindsofvortexmotionasARincreasesandvortexbifurcationoccursatacertainAR.Theprocessesofadvection,interaction,anddecayofvortexringareanalyzed.Numericalresultscoincidewithexperimentsandothernumericalsimulations.

简介：Theexistenceofinfinitelymanysolutionsfortheequation

简介：Adynamicalsystemforcomputingtheellipticboundaryproblemispresented.Itisshownthattheproposedsystemisgloballyasymptoticallystable.Thesystemcanbesimulatedbyaneuralnetwork.Simulationresultsarevalidandsatisfactory.

简介：在这份报纸，作者在homotopy上学习homologically小的symplectic组行动椭圆形的表面E(n)并且得到一些刚硬结果。

简介：有边界不安的非线性的椭圆形的方程的解决之可能性被考虑。原来的问题的使不安的答案被获得；答案的一致地有效的扩大被证明。

简介：Theauthorsstudyhomogenizationofsomenonlinearpartialdifferentialequationsoftheform-div(a(hx,h^2x,Duh))=f,whereaisperiodicinthefirsttwoargumentsandmonotoneinthethird.Inparticularthecasewhereasatisfiesdegeneratedstructureconditionsisstudied.ItisprovedthatuhconvergesweaklyinW0^1,1(Ω)totheuniquesolutionofalimitproblemash→＋∞.Moreover,explicitexpressionsforthelimitproblemareobtained.

简介：

简介：Inthispaper,usingcapacitytheoryandextensiontheoremofLipschitzfunctionswefirstdiscusstheuniquenessofweaksolutionofnonhomogeneousquasilinearellipticequationsinspaceW(θ,p)(Ω),whichisbiggerthanW1,p(Ω).Next,usingrevisereverseHolderinequalityweprovethatifωcisuniformlyp-think,thenthereexistsaneighborhoodUofp,suchthatforallt∈U,theweaksolutionsofequationcorrespondingtareboundeduniformly.Finally,wegetthestabilityofweaksolutionsonexponentp.

简介：在这份报纸，为2m-th-oder的矩形的有限元素的一个班在n尺寸的椭圆形的边界价值问题(m，n1)以一种正规方式被建议，它包括(2m-1)-thHermite插值元素(n=1)，n线性的有限元素(m=1)并且Adini元素(m=2)。nonconforming与会聚的顺序O(h2)，为把问题弄弯的板的三角形的有限元素也被建议。[从作者抽象]

简介：Thispaperfocusesonnonlocalintegralboundaryvalueproblemsforellipticdifferential-operatorequations.HeregivenconditionsguaranteethatmaximalregularityandFredholmnessinL_pspaces.TheseresultsareappliedtotheCauchyproblemforabstractparabolicequations,itsinfinitesystemsandboundaryvalueproblemsforanisotropicpartialdifferentialequationsinmixedL_pnorm.

简介：作者学习第二份订单的接口问题的答案的结构在三种空格尺寸的线性椭圆形的部分微分方程。单个点的集合由一些单个线组成；一些孤立的单个点。在一根单个线或一个单个点附近，每个弱答案能被分解成二部分，这被证明，单个部分；常规部分。单个部分是一些更简单的方程的特别答案的某有限的和，；常规部分在一些标准被围住，它在Sobolev空间H是比那稍微弱的[2]。

简介：

简介：我们在Rn为第二份订单有有限光滑的系数的椭圆形的方程。如此的结果能作为古典Lp(1

简介：TheRitzprojectionsoftheellipticproblem（?）(aij（?）ju)+c0u=finΩ,u=0on（?）Ω,andthequasilineareilipticproblem（?）（ai（x,Du））+a0（x,Du）=0inΩ,u=0on（?）Ωwithlinearfiniteelementsadmitanasymptoticerrorexpansion,respectively,forcertainclassesof“uniform”meshes.ThisprovidesthetheoreticaljustificationfortheuseofRichardsonextrapolationforincreasingtheaccuracyoftheschemefromO（h2）toO（h4|lnh|）.

简介：InthispaperweconsidertheeigenvalueproblemofsemilinearellipticequationinR~n(n≥~3)-△u+α(x)u=λf(x,u),u∈H~1(R~n).

简介：Usingvariationalmethod,theauthorsgetanexistenceresultforpositivesolutionsofasuperlinearellipticboundaryvalueproblemwithoutassumingtheP.S.condition.Toprovetheresultsinthispaper,theauthorsadoptthemethodofgradientflowanduseanewclassoftruncationfunctions.

简介：Inthispaper,someeffectivecascadicmultigridmethodsareproposedforsolvingthelargescalesymmetricornonsymmetricalgebraicsystemsarisingfromthefinitevolumemethodsforsecondorderellipticproblems.Itisshownthatthesealgorithmsareoptimalinbothaccuracyandcomputationalcomplexity.Numericalexperimentsarereportedtosupportourtheory.