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

Part of: Parabolic equations and systems Partial differential equations

Published online by Cambridge University Press:  09 August 2019

Kin Ming Hui
Kin Ming Hui*
Affiliation:
Institute of Mathematics, Academia Sinica Taipei, Taiwan, R. O. C. (kmhui@gate.sinica.edu.tw)
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Abstract

Let n ⩾ 3 and 0 < m < (n − 2)/n. We extend the results of Vazquez and Winkler (2011, J. Evol. Equ. 11, no. 3, 725–742) and prove the uniqueness of finite points blow-up solutions of the fast diffusion equation ut = Δum in both bounded domains and ℝn × (0, ∞). We also construct initial data such that the corresponding solution of the fast diffusion equation in bounded domain oscillates between infinity and some positive constant as t → ∞.

Keywords

uniquenessfast diffusion equationtime oscillating behaviour

MSC classification

Primary: 35K65: Degenerate parabolic equations
Secondary: 35B51: Comparison principles 35B40: Asymptotic behavior of solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 2849 - 2870
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Copyright
Copyright © 2019 The Royal Society of Edinburgh

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