Numerical analysis of the rescaling method for parabolic problems with blow-up in finite time

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• 作者：V.T. Nguyen¹ ; ^{vtnguyen@math.univ-paris13.fr} ; ^{Tien.Nguyen@nyu.edu}
• 关键词：Numerical blow-up ; Finite-time blow-up ; Nonlinear parabolic equations
• 刊名：Physica D: Nonlinear Phenomena
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：339
• 期：Complete
• 页码：49-65
• 全文大小：1796 K
• 卷排序：339

文摘

In this work, we study the numerical solution for parabolic equations whose solutions have a common property of blowing up in finite time and the equations are invariant under the following scaling transformation u↦uλ(x,t):=λ2p−1u(λx,λ2t). For that purpose, we apply the rescaling method proposed by Berger and Kohn (1988) to such problems. The convergence of the method is proved under some regularity assumption. Some numerical experiments are given to derive the blow-up profile verifying henceforth the theoretical results.