Camassa-Holm方程解的渐近性质.pdf

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4、AsymptoticPropertiesoftheSolutionsoftheCamassa-HolmEquationCandid

5、ateJiaJiaSupervisorProfessor.TANGTai-ManCollegeMathematicsandComputationalScienceProgramPureMathematicsSpecializationPartialDifferentialEquationDegreeMasterofScienceUniversityXiangtanUniversityDateApril22th,2011=+C

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22、uttheasymptoticpropertiesofCamassa-Holm(CH)equation.ThispaperprovesthattheasymptoticdensityofthepositivemomentumdensityoftheCHequationisacombinationofDiracmeasuressupportedonthepositiveaxis.Thismeansthatastimegoestoinfinity,momentumdensityconcentratesinsmallintervalsmovingrightwith

23、differentconstantspeeds.Thesolutionessentiallydecaysexponentiallyoutsidetheseintervals.Fromtheexistingliteratureaswellasnumericalresultsandspecialcasesofexplicitsolutions,thereareevidencesthatmanyinitialconditionsofCHequationgiverisetoatrainofsolitarywavesmovingatdifferentspeeds.Int

24、histhesis,usingthemethodofasymptoticdensity,undertheassumptionthatitisunique,wegivefurtherevidencesforthisphenomenon.SimilardiscussionsarevalidfortheDegasperis-Procesiequation.KeyWords:Camassa-Holmequation;Degasperis-Procesiequation;Asymp-toticdensity;MomentumdensityIISeV......

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