Camassa-Holm方程的初邊值問題.pdf

1、華南師范大學(xué)碩士學(xué)位論文CamassaHolm方程的初邊值問題姓名：馬世香申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：丁時進(jìn)20050601摘要：本文主要考慮一維淺水波方程(CamassaHolm方程)在半直線上的初邊值問題通過先驗估計和緊性方法獲得當(dāng)初值n?！嗜?。(R)n硪(R)時，局部強(qiáng)解的存在唯一性，以及在一定條件下的整體強(qiáng)解的存在唯一性和blow—up性質(zhì)關(guān)鍵詞：淺水波方程，初邊值問題，局部解的存在唯一性，整體解的存在唯一性，bl

2、owupAbstract：Inthispaper，WCobtaintheexistenceanduniquenessofthelo—calstrongsolutionstotheinitialboundaryvalueproblemforaonedimensionalshallowwaterequation(Camassa—Holmequation)onthehalfspacez0withinitialdatan0∈H2(R)nH0(R

3、)ThesolutionisobtainedasalimitoftheSO—lutionsfoaclassofapproximationproblemsWcalsoestablishtheglobalresultofthecorrespondingsolution，providedthattheinitialdata“osatisfiescertainpositivityconditionKeywords：shallowwaterequ