Please use this identifier to cite or link to this item: `http://hdl.handle.net/11455/90454`
DC FieldValueLanguage
dc.contributorHung-Ju Kuoen_US
dc.contributor郭紅珠zh_TW
dc.contributor.author周群zh_TW
dc.contributor.authorChen Chouen_US
dc.contributor.other應用數學系所zh_TW
dc.date2015zh_TW
dc.date.accessioned2015-12-09T06:30:10Z-
dc.identifier.citation1.L. A. Caffarrelli, A.Friedma Blow-up of solutions of nonlinear heat equations 2.C.H. Cho, S. Hamada, H.Okamoto On the finite difference approximation for a parabolic blow-up problem 3.A. Friedman, B. Mcleod Blow-up of positive solutions of semilinear heat equations 4.A. Friedman Partial differential equation of parabolic type 5.S. Ito On blow-up of positive solutions of semilinear parabolic equation 6.T. Nakagawa Blowing up of a finit difference solution to ut=uxx+u2 7.Murray H. Protter, Hans F. Weinberger Maximum principle in differential equationzh_TW
dc.identifier.urihttp://hdl.handle.net/11455/90454-
dc.description.abstractWe use the Crank-Nicolson method for the equation and then show that the numerical solution blows up as well. Moreover, We prove that the blow up time of our numerical solution tends to that of the solution when the mesh length h tends to 0.en_US
dc.description.abstract針對此非線性拋物型偏微分方程式，我們給予克蘭克-尼克爾森方法來討論方程式的解以及其具數值解的爆炸性問題。在適度的初始條件假設下， 此兩種解都在有限的時間內其L2 norm趨近於無窮大。在此論文我們也證明當網格長度趨近於零時數值解的爆炸時間會趨近原方程式解的爆炸時間。zh_TW
dc.description.tableofcontents一、Introduction 1 二、Preliminaries 2 三、The Crank-Nicolson Scheme 5 四、Construction of the Crank-Nicolson schemes 12 五、The Blow up times of the exact and approximation solutions 16 六、Further Research 20 七、Reference 21zh_TW
dc.language.isoen_USzh_TW
dc.rights同意授權瀏覽/列印電子全文服務，2018-07-28起公開。zh_TW
dc.subject爆炸zh_TW
dc.subject非線性拋物方程zh_TW
dc.subjectBlows upen_US
dc.subjectNonlinear parabolic equationen_US
dc.titleOn blow up of nonlinear parabolic equation and their C-N methodsen_US
dc.title非線性拋物方程式及其C-N方法的爆炸問題zh_TW
dc.typeThesis and Dissertationen_US
dc.date.paperformatopenaccess2018-07-28zh_TW
dc.date.openaccess2018-07-28-
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