一類半線性雙曲型方程解的存在唯一性.pdf

1、西南交通大學碩士學位論文一類半線性雙曲型方程解的存在唯一性姓名：李怡申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：楊晗20090401西南交通大學碩士研究生學位論文第1I頁AbstractTheCauchyproblemforthefollowingsemi—linearweaklyhyperbolicequationsisdiscussedinthispaperk—t2tAu=F(u，Vu)l(“(o，)，比，(o，))一(“o，“，)T

2、heexistenceandtheuniquenessofclassicalsolutionsisstudiedFirstlythelinearweaklyhyperbolicequationisstudiedbyusingthepropertyofL，spaeceandSobolevspaeceSecondlyonthebaseofaboveestimates，afunctionspaceisdefinedandsomeimporta

3、ntinequalitiesareusedtoestimatethenonlinearitemsFinallywiththehelpoftheBanach’Sfixedpointtheorem，theexistenceanduniquenessofclassicalsolutionsofthesemilinearweaklyhyperbolicequationateprovedThisarticleisorganized弱follows

4、，inChapter1，thebackgroundandoartentdeve10pmentforwaveequationsateintroducedThenthemainresults弱theirprincipalresultsategiveninChapter2TherelativelemmasfortheproofofthemainTheoremsateintroducedinChapter3andthetwoprincipalr