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標題: On blow up of nonlinear parabolic equation and their C-N methods
作者: 周群
Chen Chou
關鍵字: 爆炸;非線性拋物方程;Blows up;Nonlinear parabolic equation
引用: 1.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 equation
We 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.

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。
Rights: 同意授權瀏覽/列印電子全文服務,2018-07-28起公開。
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