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页数:31页
时间:2019-05-15
《带时滞项阻尼Kirchhoff方程的反向吸引子》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、独创性声明本人声明所呈交的论文是我个人在导师指导下进行的研究工作及取得的研究成果.除了文中特别加以标注和致谢的地方外,论文中不包含其他人或集体已经发表或撰写过的研究成果,对本文的研究做出贡献的集体和个人均已在论文中作了明确的说明并表示了谢意.研究生签名:论文使用和授权说明本人完全了解云南大学有关保留、使用学位论文的规定,即:学校有权保留并向国家有关部门或机构送交学位论文和论文电子版;允许论文被查阅或借阅;学校可以公布论文的全部或部分内容,可以采用影印、缩印或其他复制手段保存论文.(保密的论文在解密后应遵循此规定)研究生签名:新躲姬日本人及导师同意将学位论文提交至清华大学“中国学术期刊(光
2、盘版)电子杂志社”进行电子和网络出版,并编入CNKI系列数据库,传播本学位论文的全部或部分内容,同意按《中国优秀博硕士学位论文全文数据库出版章程》规定享受相关权益.‘研究生签名:导师签名:——日期:摘要本文主要研究了带时滞项阻尼Kirchhoff方程的解和反向吸引子存在性睾埘罢删V“
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4、2)△甜=厂+岫f),防u(x,f)lr=o,f≥f一,u(x,f)=①(x,t-r),x∈Q,f∈[r—r,r】静r)=詈(硝一r),xeQ,ts[一,叫其中f+h(t,“,)是具有记忆解的能量等式,a>0,①是定义在区间【r一,.,f】上的初始值其中r>0,%(0)=u(t+O),0∈【一r,0】.对
5、任意s∈R有06、唯一性.第四章主要证明空间吸引集的存在性和空间吸收集的存在性,从而证明时滞项阻尼Kirchhoff方程反向吸引子的存在性.关键词:Kirchhoff方程:存在唯一性:反向吸引子AbstractThispapermainlydiscusstheexistenceofsolutionandpullbackattractorsforadampedKirchhoffequationwithdelays窘埘詈删vull2)址Ⅲ(埘抄fu(x,,)lr=0,t>r-ru(x,f)=①(x,f—r),x∈Q,,∈【r—M】和,)=詈(彬一r)艇蛳∈r-r,r】Wheref+h(t,“r)istheso7、urceintensitywhichmaydependonthehistoryofthesolution,aisainitialdatumontheinterval[r一,.,r]wherer>o,甜,isdefinedfor0∈【一r,O]asut(0)=zf(f+9).Foranys∈R,wehave08、r,weleadintotheclassicphysicalmodeloftheKirchhoffequationonthebasisofthenon-autonomouswaveequationwithdelays,mainlydiscusstheexistenceofthesolutionandtheexistenceofthepullbackattractorsforadampedKirchhoffequationwithdelay.Thispapermainlyconsistsofthefollowingfourchaptersdiscussstheexistenceofpull9、backattractorsofthedampedKirchhoffequationwithdelays.Inthefirstchapter,wemainlyintroducesthestudybackgroundandsituationofpullbackattractors.Inthesecondchapter,wemainlyintroducessomebasicconceptsandcommonlyusedinequalit
6、唯一性.第四章主要证明空间吸引集的存在性和空间吸收集的存在性,从而证明时滞项阻尼Kirchhoff方程反向吸引子的存在性.关键词:Kirchhoff方程:存在唯一性:反向吸引子AbstractThispapermainlydiscusstheexistenceofsolutionandpullbackattractorsforadampedKirchhoffequationwithdelays窘埘詈删vull2)址Ⅲ(埘抄fu(x,,)lr=0,t>r-ru(x,f)=①(x,f—r),x∈Q,,∈【r—M】和,)=詈(彬一r)艇蛳∈r-r,r】Wheref+h(t,“r)istheso
7、urceintensitywhichmaydependonthehistoryofthesolution,aisainitialdatumontheinterval[r一,.,r]wherer>o,甜,isdefinedfor0∈【一r,O]asut(0)=zf(f+9).Foranys∈R,wehave08、r,weleadintotheclassicphysicalmodeloftheKirchhoffequationonthebasisofthenon-autonomouswaveequationwithdelays,mainlydiscusstheexistenceofthesolutionandtheexistenceofthepullbackattractorsforadampedKirchhoffequationwithdelay.Thispapermainlyconsistsofthefollowingfourchaptersdiscussstheexistenceofpull9、backattractorsofthedampedKirchhoffequationwithdelays.Inthefirstchapter,wemainlyintroducesthestudybackgroundandsituationofpullbackattractors.Inthesecondchapter,wemainlyintroducessomebasicconceptsandcommonlyusedinequalit
8、r,weleadintotheclassicphysicalmodeloftheKirchhoffequationonthebasisofthenon-autonomouswaveequationwithdelays,mainlydiscusstheexistenceofthesolutionandtheexistenceofthepullbackattractorsforadampedKirchhoffequationwithdelay.Thispapermainlyconsistsofthefollowingfourchaptersdiscussstheexistenceofpull
9、backattractorsofthedampedKirchhoffequationwithdelays.Inthefirstchapter,wemainlyintroducesthestudybackgroundandsituationofpullbackattractors.Inthesecondchapter,wemainlyintroducessomebasicconceptsandcommonlyusedinequalit
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