一類非線性波動方程的初邊值問題.pdf

1、編號：碩士學(xué)位論文碩士學(xué)位論文題目：一類非線性波動方程的初邊值問題培養(yǎng)單位：數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院專業(yè)名稱：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：李德生教授研究生：張哲完成時間：2015年1月10日沈陽師范大學(xué)研究生處制類別全日制研究生√教育碩士同等學(xué)力TheinitialboundaryvalueproblemofaclassofnonlinearwaveequationsAbstractThisdissertationmainlyinvestigatest

2、hefollowingpropertiesofsolutionsofaclassofwaveequationswithanonlinearsourcetermadampingterm.Itcontainstheproblemsofexistenceofsolutionsfinitetimeblowup.Δ2?Δ?Δ=()()∈Ω0∞)，(0)=0()，(0)=1()∈Ω，()=0，()∈Ω(0).WhereΩ??isaboundeddo

3、mainwithsmoothboundary?Ω，()isunknownfunction，ΔistheLaplaceoperat.Thisthesisconsistsoffourparts：Inthefirstchapter，somephysicalbackgroundwillbeintroducedofthenonlinearpartialdifferentialequationswithinitialboundaryvaluepro

4、blem.Simultaneously，someavailableresultswillbesurveyedsofar.Inthesecondchapter，westudythisfthdernonlinearwaveequationwiththeinitialboundaryvalueproblemtheexistenceoftheglobalweaksolutionstothisproblemisprovedbymeansofthe

5、potentialwellmethodtheGalerkinmethod.Thechapter3dealswiththeinitialboundaryvalueproblemfaclassoffourthderdampednonlinearwaveequations.Byusingthepotentialwellmethod，someresultsofblowupsolutionswithcertaininitialprofilesar

6、eestablished.Inchapter4，weinvestigatethefinitetimeblowupproblemsfthenonlinearwaveequationwiththeinitialboundaryvalueproblemwhenγ=0，()=||?1athighenergylevel.Byemployingthepotentialwellmethod，thisthemegivesthatfwhichinitia