简介：TheregularsolutionsoftheisentropicEulerequationswithdegeneratelineardampingforaperfectgasarestudiedinthispaper.Andacriticaldegeneratelineardampingcoefficientisfound,suchthatifthedegeneratelineardampingcoefficientislargerthanitandthegasliesinacompactdomaininitially,thentheregularsolutionwillblowupinfinitetime;ifthedegeneratelineardampingcoefficientislessthanit,thenundersomehypothesesontheinitialdata,theregularsolutionexistsglobally.

简介：ThepaperdealswiththestronglydampednonlinearwaveequationofKirchhofftype.Theexistenceofaglobalattractorisprovenbyusingthedecomposition,andmoreover,thestructureoftheglobalattractorisestablished.Ourresultsimprovethepreviousresults.

简介：Inthispaper,weconsiderthepartialdifferentialequationofanelasticbeamwithstructuraldampingbyboundaryfeedbackcontrol.First,weprovethisclosedsystemiswell--posed;thenweestablishtbeexponentialstabilityforthiselasticsystembyusingatheoremwhichbelongstoF.L.Huang;finally,wediscussthedistributionandmultiplicityofthespectrumofthissystem.Theseresultsareveryimportantandusefulinpracticalapplications.

简介：<正>AnonlinearhingedextensibleelasticbodyequationwithstrongstructuraldampingandBalakrishnan-Taylordampingoffullexponentisstudiedasageneralmodelforlargespacestructuresofhigherdimensions.Inthispaper,theabsorbingsetsandfiatinertialmanifoldareobtainedforthisnonlinearbodyequation.Thecontrolspilloverproblemassociatedwiththestabilizationofthisequationisresolvedbyconstructingalinearfinitedimensionalfeedbackcontrolbasedontheexistenceofinertialmanifoldsoftheuncontrolledequation.Moreover,theresultsobtainedarerobustwithrespecttotheuncertaintyinstructuralparameters.

简介：Thequasilinearhyperbolicequationwithnonlineardampingisconsideredinthispaper,anewasymptoticprofileforthesolutiontotheequationisobtainedbysuitablychoosingtheinitialdataofthecorrespondingparabolicequation,theconvergenceratesofthenewprofilearebetterthanthatobtainedbyNishihara(1997,J.DifferentialEquations137,384-395)andH.-J.Zhao(2000,J.DifferentialEquations167,467-494).

简介：在这份报纸，我们考虑与一般抑制联系到线性有弹性的方程的一个半线性的概括夸张边界价值问题可变代表的术语和非线性打字。在合适的条件下面，本地、全球的存在定理被证明。答案的唯一被消除被另外的作者为不同特别问题强加了的一些假设得到了。我们证明有重要起始的资料的任何答案变得稳定。

简介：这份报纸是一个continue工作[4,5]。在以前的二份报纸，我们与看情况时间的抑制术语学习了多维的可压缩的Euler方程的Cauchy问题--(1+t)u，在此0并且>0是常数。我们显示出那，为所有0并且>0，Cauchy问题的光滑的答案全球性存在或在有限时间骤起。在现在的纸，而不是Cauchy问题，我们在一半考虑起始边界的价值问题空间有空间尺寸d=的d+2,3。在方程和液体涡度的特殊结构的帮助下，我们克服困难从边界效果产生。我们证明那在那里存在0的一个全球光滑的解决方案<1当起始的数据接近它的平衡状态时。另外，液体涡度的指数的腐烂将也被建立。

简介：Thispaperpresentsaclassofr-point(r+1)st-orderA-stableone-blockmethodswithdampingattheinfinitepoint(DIAOBr,r+1).Undertheconditionsofthesameorder,A-stabili-ty,operationcount(ateachiterativestep)andstoragespacearethesameasthemethodsin[19],themethodsinthepaperimprovethestabilityinaneighborhoodattheinfinitepoint.And,byus-ingtheOOPImethod[20],itpossessesmuchfasterrateofconvergenceforsolvingsystemsofnon-linearequationsproducedbytheDIAOBr,r+1.