非線性色散方程初邊值問(wèn)題解的研究.pdf

1、非線性色散方程初邊值問(wèn)題解的研究Thestudyforthesolutionofnonlineardispersionequationwiththeinitialboundaryvalue作者：楊珍珍Author：Zhenzhen—————Y——————a————n，————g——指導(dǎo)教師：墜全選一Supervisor：』i旦魚(yú)里魚(yú)旦望g專業(yè)：基礎(chǔ)數(shù)學(xué)Major：學(xué)位：理學(xué)嗄Degree：授予單位：浙江師范大學(xué)PureMathemati

2、csMasterofScienceInstitute：——ZhejiangNormalUniversity——May，2016AbstractInthispaperweconsidertheinitialboundaryvalueproblemofsemilinearSchrSdingereauationonhalflineBlowupresultwillbeestablished，assumingthepowerofthenon—li

3、neartermsatisfying1P≤2Theproofisbasedonacontradictionargument，byconstructingaspecialtestfunctionTheconclusionaredividedinto1P2andP=2toDroveandweobtaintheupperboundofthelifespaninthecase1P2Further—moreⅥ，eestablishblowupth

4、eoremsforcriticalsemilinearwaveequationswithfocusingnonlineartermin3一Dboundeddomains，forbothDirichletanddissipativeboundaryconditionsTheproofisbasedontheconcavitymethodThispaperconsistsofthreechaptersThefirstchapteristhe

5、introductionItmainlyintroducestheresearchbackground，situationandresearchsignificanceofSchr6dingerequation，thewaveequationandthenecessityanditsimportantmeaningoftheexistenceofthetestfunction，givingthepreliminariesandmainc

6、ontentofthispaperThesecondchapterapplythetestfunctionmethod毋(t，互)=cz科(z)T一。(1一亍t，k“andthecontradictionargumenttoprovetheblowupandlifespanestimateforonedimensionalsemilinearSchr6dingerequationwithinitialboundaryvalueBlowu

7、presultwillbeestablished，assumingtheFurthermore，weobtaintheupperP2powerofthenonlineartermsatisfying1P≤boundofthelifespanT(E)SG￡昂inthecase1∞一lThethirdchapterintroducetheconcavitymethodtoprovetheblowuptheoremsforcriticalse