简介:Inthispaper,usingcapacitytheoryandextensiontheoremofLipschitzfunctionswefirstdiscusstheuniquenessofweaksolutionofnonhomogeneousquasilinearellipticequationsinspaceW(θ,p)(Ω),whichisbiggerthanW1,p(Ω).Next,usingrevisereverseHolderinequalityweprovethatifωcisuniformlyp-think,thenthereexistsaneighborhoodUofp,suchthatforallt∈U,theweaksolutionsofequationcorrespondingtareboundeduniformly.Finally,wegetthestabilityofweaksolutionsonexponentp.
简介:Foraclassofmixedinitial-boundaryvalueproblemforgeneralquasilinearhyperbolicsystems,thispaperestablishesthelocalexactboundarycontrollabilitywithboundarycontrolsonlyactingononeend.Asanapplication,theauthorsshowthelocalexactboundarycontrollabilityforakindofnonlinearvibratingstringproblem.
简介:ThispaperconsidersthepointwiseestimateofthesolutionstoCauchyproblemforquasilin-earhyperbolicsystems,whichbasesontheexistenceofthesolutionsbyusingthefundamentalsolutions.Itgivesasharppointwiseestimatesofthesolutionsondomainunderconsideration.Specially,theestimateispreciseneareachcharacteristicdirection.
简介:Inthispaper,thefirstboundaryvalueproblemforquasilinearequationoftheform△A(u,x)+m∑i=1(e)bi(u,x)/(e)xi+c(u,x)=0,Au(u,x)≥0isstudied.Byusingthecompensatedcompactnesstheory,someresultsontheexistenceofweaksolutionareestablished.Inaddition,undercertainconditiontheuniquenessofsolutionisproved.
简介:Thispaperconcernswithexistenceofgeneralizedsolutionsoffirstboundaryvalueproblemforakindofstronglydegeneratequasilinearparabolicequations.TheauthorassumesthatthecoefficientsintheequationsatisfystronglydegeneratemonotoneconditionandotherweakenedconditionscomparingwiththoseofLadyzenskaja’s.Anexistencetheoremisgivenandproved.
简介:Anonlineardifferenceschemeisgivenforsolvingaquasilinearsiagularlyperturbedtwo-pointboundaryvalueproblemwithaturningpoint.Themethodusesnon-equidistantdiscretizationmeshes.ThesolutionoftheschemeisshowntobefirstorderaccurateinthediscreteL^∞norm,uniformlyintheperturbationparameter.
简介:THEPATHWISESOLUTIONFORACLASSOFQUASILINEARSTOCHASTICEQUATIONSOFEVOLUTIONIN BANACHSPACEⅡHuYaozhong(WuhanInst.ofMath.Sci.,Chin.A...
简介:Groupclassificationofquasilinearthird-orderevolutionequationsisgivenbyusingtheclassicalinfinitesimalLiemethod,thetechniqueofequivalencetransfor-mations,andthetheoryofclassificationofabstractlow-dimensionalLiealgebras.WeshowthattherearethreeequationsadmittingsimpleLiealgebrasofdimensionthree.Allnon-equivalentequationsadmittingsimpleLiealgebrasarenothingbutthesethree.Furthermore,wealsoshowthatthereexisttwo,five,twenty-nineandtwenty-sixnon-equivalentthird-ordernonlinearevolutionequationsadmittingone-,two-,three-,andfour-dimensionalsolvableLiealgebras,respectively.
简介:我们学习二维的non-self-similar的一个家庭的单个结构quasilinear的全球解决方案和他们的相互作用夸张能量守恒定律。当起始的断绝在仅仅上发生时,为盒子,二拆散统一圆和起始的数据是二个不同经常的状态,全球答案被构造,一些新现象被发现。在分析,我们首先为0t构造答案
简介:ThepurposeofthispaperistouseaveryrecentthreecriticalpointstheoremduetoBonannoandMaranotoestablishtheexistenceofatleastthreesolutionsforthequasilinearsecondorderdifferentialequationonacompactinterval[a,b]?R{-u’’=(λf(x,u)+g(u))h(u’),in(a,b),u(a)=u(b)=0underppropriatehypotheses.Weexhibittheexistenceofatleastthree(weak)solutionsand,andtheresultsareillustratedbyexamples.
简介:Inthispaper,weusetheupper-lowersolutionmethodwiththetheoryofmonotoneoperatorstoobtaintheexistenceofcoupledweakquasi-solutionsofthefollowingboundaryvalueproblemforquasilinearellipticsystem