Uniqueness and time oscillating behaviour of finite points blow-up\n solutions of the fast diffusion equation

2018/05/26 by Kin Ming Hui, Hui, Kin Ming
Computer Science · Mathematics · #35B40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Primary 35K65 Secondary 35B51

paper · pdf · doi:10.48550/arxiv.1805.11449

openalex publication_date 2018/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n\≥ 3 and 0<m<\(n-2)/(n). We will extend the results of J.L.\nVazquez and M. Winkler and prove the uniqueness of finite points blow-up\nsolutions of the fast diffusion equation u_t=\Δ u^m in both bounded\ndomains and \ℝⁿ\× (0,\∞). We will also construct initial\ndata such that the corresponding solution of the fast diffusion equation in\nbounded domain oscillate between infinity and some positive constant as\nt\→\∞.\n

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