degasperis-procesi方程整体弱解大时间性态

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1、Degasperis-Procesi2010-5-26OntheLargeTimeBehaviorofGlobalWeakSolutionstotheDegasperis-ProcesiEquationCandidateZhangNanaSupervisorandRankAssociateProfessor.TangTai-ManCollegeProgramSpecializationDegreeUniversityDateMathematicsandComputationalSciencePureMathematicsPartialDifferentialEquationMa

2、sterofScienceXiangtanUniversityMay26th,2010,...,.,,.,..Degasperis-Procesi,u0∈H1(R)∩L3(R)(u0−u0,xx)∈M+(R),W1,∞(R+×R)∩Lloc(R+;H1(R))...Degasperis-Procesi.,;,;;:Degasperis-Procesi;;.I∞AbstractFortheCauchyproblemofone-dimensionalDegasperis-Procesiequation,whentheinitialconditi

3、onu0belongstoH1(R)∩L3(R)and(u0−u0,xx)belongstoM+(R),itsW1,∞(R+×R)∩Lloc(R+;H1(R))globalweaksolutionexists.Inthispaper,westudythelargetimebehaviorofsuchglobalweaksolution.Thispaperisdividedintofourparts.Inthefirstpart,wegiveanintroductiontotheproblemandthestatetheorem.Inthesecondchapter,weintrod

4、ucesomeresultswhichwe’lluselater.Inthethirdchapter,weanalyzethelargetimebehavioroftheglobalweaksolutiontotheDegasperis-Procesiequation.Finally,weconcludewithafewquestionsforfurtherinvestigations.keywords:Degasperis-Procesiequation;globalweaksolution;largetimebe-haviorII∞......................

5、.............................................IAbstract................................................................II.......................................................11.11.21.32.12.2.....................................................1................................1..............

6、.......................................3.................................................4...........................................4.....................................................5Degasperis-Procesi.......8.................................................17...........................

7、..................................18................................................................21..........................22III§1.1Degasperis-Procesi2+∞0(1.1)∂tu−∂t∂x2u+4u∂xu=3∂xu∂x2u+u∂x3u,u(0,x)=u0(x),x∈R1.W1,∞(R+×R)∩Lloc(R+;H1(R