帶有局部化反應(yīng)項(xiàng)和自由邊界的反應(yīng)擴(kuò)散系統(tǒng)的若干性質(zhì).pdf

1、目錄摘要l摘要2章引言4早jIi“41研究工作的背景及發(fā)展概況412本文的主要工作9第二章具有局部化反應(yīng)項(xiàng)的自由邊界問(wèn)題lO21問(wèn)題的引入及描述1O22解的局部存在性和唯一性l123有限爆破18第三章全局快解和慢解的存在性2131全局快解2l32全局慢解23參考文獻(xiàn)28讀學(xué)位期間發(fā)表的學(xué)術(shù)論文目錄32致謝33揚(yáng)州大學(xué)學(xué)位論文原創(chuàng)性聲明和版權(quán)使用授權(quán)書(shū)34AbstractWitllthedevelopmentofmodemsciencea

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3、andSOonThesekindsofequations(systems)arenotallcontinuouslysolvableastimeincreases，becausesomesolutionsbecomeunboundedinfinitetimeInnumericalcalculations，wealsofindt1atbl。wupOCCURfrequentlyTherefore，itsofgreatimp。rtancean

4、dnaturalthe。reticallyforuStofi黜ouIunderwhatconditionsblowupOCCURS，theglobalsolutionexistsFunhe珊ore，whenthegl。bals。luti。nexists，what’sofgreatsignificancehereistomakecleartlle1。ngtimebehaviorsofthesolutionManyscholarshaves

5、tudiedtheblowupproblemsinafixedboundeddomaininonedimenslonalcaseormultipledimensionalcase，aswellasthecorrespondingCauchyproblemNow，WeconsidertheintermediatecasebetweenthecasesofboundedaIldunboulldedintervalsfreeboundaryp

6、roblem，whichisthecoreofthispaperandwewillgivethespecificmodellaterFreeboundaryproblemisalwaysadifficultproblem，astheboundaryisuI】婦ownandiscn￡mgingastlmeIncreasesAndwewillfigureoutthefreeboundarytogether、析ththesolutionf’r

7、eebound哪problemisdifferentfromthegrowingdomainproblem，inwhichthebourldarvischangingaccordingtoaknownfunctionTomakethispresentationmorereadableandsystematic，weconcemsprim撕lywitllanonlinearreactiondiffusionmodelwithalocali

8、zedreactiontermandfreebollIldadesandmequalitativepropertiesofthesemodelsareextensivelystudiedItconsistsofthreepansInthefirStpart，wemainlyintroducethebackgroundandhistoryabouttherelated、ⅣorkThesecondpartisdevotedtoanonlin

9、earreactiondiffusionmodelwithalocalizedreactiontermandfreeboundariesinonedimensionandwemainlygivethefollowingresuIts：firstly，thelocalexlstencea11duniquenessofaclassicalsolutionisgivenOnthesecondplace，weprovethatthesoluti

10、onceasestoexistundercertainconditionsAndOURresultsindicatetlatblo、礬lpOCCURSiftheinitialdataissufficientlylargeThethirdpartmainlydealswiththeexistenceofglobalfastsolutionand鰣obalslowsolutionOurresultsshowthatwhentheinitia