两类偏微分方程的解的性质研究.pdf

山 西 大 学 2015届硕士学位论文两类偏微分方程的解的性质研究作 者 姓 名 兰 杰指 导 教 师 郝 江 浩 教 授 学 科 专 业 运 筹 学 与 控 制 论 研 究 方 向 非 线 性 偏 微 分 方 程 培 养 单 位 数 学 科 学 学 院学 习 年 限 2012年9月 至2015年6月二◦一五年六月Thesis for Master’s degree, Shanxi University, 2015.Study on the properties of solutions of two classes of partial differential equationsS t u d en t Nam eSu p ervis o rM aj o rField o f Res earch D e p art m en t Res earch D u rat io nJie LanPro f . Jian g h ao HaoOp erat io n al Res earch an d Co n t ro l Th eo ry No n lin ear Part ial Dif f eren t ial Equ at io n Sch o o l o f Mat h emat ical Scien ces 2012.09-2015.06Ju n e, 2015目 录蚊觀........................................................................................................................................iAbs t ract ...................................................................................................................................... ii1一^ X 0 .................................................................................................................................1第二章一类Eu ler-Bern o u lli板方程解的性质....................................................................4§ 2.1弓 丨 言............................................................................................................................... 4§ 2.2局部存在性................................................................................................................. 5§ 2.3 y = 0时解的爆破.....................................................................................................11§ 2.4当m = 2时解的爆破................................................................................................16§ 2.5解的整体存在性.......................................................................................................21§ 2.6解的渐近稳定性.......................................................................................................22第三章一类非线性波动方程解的爆破................................................................................27§ 3.1 引言..............................................................................................................................27§ 3.2解的爆破.....................................................................................................................28参 考 文 献.....................................................................................................................................32研 究 成 果.....................................................................................................................................35翻t ............................................................................................................................................. 36个人简况及联系方式................................................................................................................37« 關..........................................................................................................................................38学位论文使用授权声明............................................................................................................39ContentsAbs t ract in Ch in es e ................................................................................................................. iAbs t ract ...................................................................................................................................... iiCh ap t er 1 P ref ace.....................................................................................................................1Ch ap t er 2 Th e p ro p ert ies o f t h e s o lu t io n s o f a clas s o f Eu ler - Bern o u lli p lat e equ at io n ........................................................................................................................................ 42.1 In t ro d u ct io n ...................................................................................................................42.2 Lo cal Exis t en ce o f t h e s o lu t io n ....................................................................................52.3 Blo w-u p o f t h e s o lu t io n f o r 7 = 0 .............................................................................. 112.4 Blo w-u p o f t h e s o lu t io n f o r m = 0 .............................................................................162.5 Glo bal Exis t en ce o f t h e s o lu t io n ................................................................................ 212.6 As ymp t o t ic St abilit y o f t h e s o lu t io n ......................................................................... 22Ch ap t er 3 Th e blo w-u p o f t h e s o lu t io n o f a clas s o f n o n lin ear wave equ at io n 273.1 In t ro d u ct io n ................................................................................................................. 273.2 Blo w-u p o f t h e s o lu t io n .............................................................................................. 28Ref eren ces ..............................。