简介:Thewaveequationwithvariablecoefficientswithanonlineardissipativeboundaryfeedbackisstudied.BytheRiemanniangeometrymethodandthemultipliertechnique,itisshownthattheclosedloopsystemdecaysexponentiallyorasymptotically,andhencetherelationbetweenthedecayrateofthesystemenergyandthenonlinearitybehaviorofthefeedbackfunctionisestablished.
简介:AD(Alternatingdirection)Galerkinschemesford-dimensionalnonlinearpseudo-hyperbolicequationsarestudied.Byusingpatchapproximationtechnique,ADprocedureisrealized,andcalculation,workissimplified.ByusingGalerkinapproach,highlycomputationalaccuracyiskept.Byusingvariousprioriestimatetechniquesfordifferentialequations,difficultycomingformnon-linearityistreated,andoptimalH^1andL^2convergenceprop-ertiesaredemonstrated.Moreover,althoughalltheexistedADGalerkinschemesusingpatchapproximationarelimitedtohaveonlyoneorderaccuracyintimeincrement,yettheschemesformulatedinthispaperhavesecondorderaccuracyinit.ThisimpliesanessentialadvancementinADGalerkinaualysis.
简介:这份报纸与推迟的中子和一般边界条件处理一个非线性的运输方程。我们建立,经由Lp-spaces(1p<+)。本地、非本地的进化问题被讨论。
简介:InthispaperweanalyzetheoptimalcontrolproblemforaclassofaffinenonlinearsystemsundertheassumptionthattheassociatedLiealgebraisnilpotent.TheLiebracketsgeneratedbythevectorfieldswhichdefinethenonlinearsystemrepresentaremarkablemathematicalinstrumentforthecontrolofaffinesystems.Wedeterminetheoptimalcontrolwhichcorrespondstothenilpotentoperatorofthefirstorder.Inparticular,weobtainthecontrolthatminimizestheenergyofthegivennonlinearsystem.Applicationsofthiscontroltobilinearsystemswithfirstordernilpotentoperatorareconsidered.
简介:ThedynamicalcharacterforaperturbedcouplednonlinearSchrodingersystemwithperiodicboundaryconditionwasstudied.First,thedynamicalcharacterofperturbedandunperturbedsystemsontheinvariantplanewasanalyzedbythespectrumofthelinearoperator.Thentheexistenceofthelocallyinvariantmanifoldswasprovedbythesingularperturbationtheoryandthefixed-pointargument.
简介:Oneofthemostinterestingproblemsofnonlineardifferentialequationsistheconstructionofpartialsolutions.Anewmethodispresentedinthispapertoseekspecialsolutionsofnonlineardiffusionequations.ThismethodisbasedonseekingsuitablefunctiontosatisfyBernolliequation.Manynewspecialsolutionsareobtained.
简介:Thispaperproposesasortofnewnormalformsconsistingofobserverformandcontrollableformfornonlinearsystems.Theconditionsfortransformingtothesenormalformsaregiven,respectively.Thesenormalformsareusedtotreattheproblemsofobserverdesignandlinearization.Thefirstpartofthispaperdealswiththeobserverform,andthesecondthecontrollableform.
简介:Existenceofsolutionsforsemiboundednonlinearevolutionequationsisestablished.Thisgivesmoreaccurateestimateofsolutionsandconditionsofexistenceaxemoreeasilyvalidated.OurresultsaresuccessfullyappliedtoproveexistenceanduniquenessofsolutionsforsomeKdVtypeequations.
简介:Inthispaper,weinvestigatethesemiclassicallimitofthegeneralizednonlinearSchr?dingerequationforinitialdatawithSobolevregularity.Also,wewillanalyzethestructureofthefluiddynamicalsystemwithquantumeffectcorrespondingtothesemiclassicallimitofthegeneralizednonlinearSchr?dingerequation.
简介:Volterraseriesisapowerfulmathematicaltoolfornonlinearsystemanalysis,andthereisawiderangeofnonlinearengineeringsystemsandstructuresthatcanberepresentedbyaVolterraseriesmodel.Inthepresentstudy,therandomvibrationofnonlinearsystemsisinvestigatedusingVolterraseries.Analyticalexpressionswerederivedforthecalculationoftheoutputpowerspectraldensity(PSD)andinput-outputcross-PSDfornonlinearsystemssubjectedtoGaussianexcitation.Basedontheseexpressions,itwasrevealedthatboththeoutputPSDandtheinput-outputcrossPSDcanbeexpressedaspolynomialfunctionsofthenonlinearcharacteristicparametersortheinputintensity.Numericalstudieswerecarriedouttoverifythetheoreticalanalysisresultandtodemonstratetheeffectivenessofthederivedrelationship.TheresultsreachedinthisstudyareofsignificancetotheanalysisanddesignofthenonlinearengineeringsystemsandstructureswhichcanberepresentedbyaVolterraseriesmodel.
简介:NonlinearMHDKelvin-Helmholtz(K-H)instabilityinapipeistreatedwiththederiva-tiveexpansionmethodinthepresentpaperThelinearstabilityproblemwasdiscussedinthepastbyChandrasekhar(1961)andXuetal.(1981).Nagano(1979)discussedthenonlinearMHDK-Hinstabilitywithinfinitedepth.Heusedthesingularperturbationmethodandextrapolatedtheob-tainedsecondordermodifierofamplitudevs.frequencytoseekthenonlineareffectontheinstabilitygrowthrateγ.However,inourview,suchanextrapolationisinappropriate.Becausewhentheinstabili-tysetsin,thegrowthratesofhigher,ordertermsontherighthandsideofequationswillexceedthecor-respondingsecularproducingterms,sotheexpansionwillstillbecomemeaninglessevenifthesecularproducingtermsareeliminated.Mathematicallyspeaking,it’simpossibletoderiveformula(39)whenγ02isnegativeinNagano’spaper.Moreover,evenasearlyasγ02→O+,theexpansionbe-comesinvalidbecausethe2ndordermodifierγ2(inhisformula(56))tendstoinfinity.Thisweak-nessisremovedinthispaper,andtheresultisextendedtothecaseofapipewithfinitedepth.
简介:Inthispaper,amodifiednonlineardynamicinequalityontimescalesisusedtostudytheboundednessofaclassofnonlinearthird-orderdynamicequationsontimescales.Thesetheoremscontainasspecialcasesresultsfordynamicdifferentialequations,differenceequationsandq-differenceequations.