若干非线性双曲方程的整体解的存在性与能量衰减.pdf

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1、山西大学2017届博士学位论文若干非线性双曲方程的整体解的存在性与能量衰减作者姓名吴密景指导教师李胜家教授学科专业基础数学研究方向偏微分方程培养单位数学科学学院学习年限2007.09-2017.06二零一七年六月Thesisforthe2017Doctor’sDegreeofShanxiUniversityGlobalexistenceandenergydecayofsolutionsforsomenonlinearhyperbolicequationsNameMijingWuSupervisorProf.ShengjiaLi

2、MajorFundamentalMathematicsFieldofResearchPartialDifferentialEquationDepartmentSchoolofMathematicalSciencesResearchDurationSep.2007–Jun.2017June,2017目录目目目录录录中文摘要.................................................................iABSTRACT...............................

3、....................................ii第一章引言....................................................................1第二章非线性双曲方程整体解的存在性与不存在性..........................112.1准备工作..................................................................112.2具有临界势函数的非线性波动方程的整体解存在的临界指数

4、............122.3具有分数阶积分的半线性阻尼双曲系统的整体解存在的临界指数.......222.4具有非零初值的半线性波动方程整体解的不存在性......................30第三章具有结构阻尼的弹性系统的能量衰减估计............................383.1问题陈述与假设...........................................................383.2具有结构阻尼的弹性系统的能量衰减估计....................

5、............393.3分数阶阻尼弹性系统的最优能量估计.....................................49参考文献........................................................................56攻读博士学位期间的主要研究成果.............................................64致谢....................................................

6、........................65个人简况及联系方式............................................................66承诺书........................................................................67学位论文使用授权声明.........................................................68–i–若干非线性双曲方程的整体解的存在性与能量

7、衰减ContentsAbstract(inChinese)...............................................................iAbstract(inEnglish)...............................................................iiChapter1Introduction...........................................................1Chapter2G

8、lobalexistenceandnonexistenceofsolutionstothenon-linearhyperbolicequations........................................................112.1Pre