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

Published online by Cambridge University Press:  09 August 2019

Kin Ming Hui*
Affiliation:
Institute of Mathematics, Academia Sinica Taipei, Taiwan, R. O. C. ([email protected])

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 → ∞.

Type
Research Article
Copyright
Copyright © 2019 The Royal Society of Edinburgh

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