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time oscillating behaviour

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Uniqueness and time oscillating behaviour of finite points blow-up solutions of the fast diffusion equation
Part of
- Partial differential equations
- Parabolic equations and systems
Kin Ming Hui
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 6 / December 2020

Published online by Cambridge University Press:

09 August 2019, pp. 2849-2870

Print publication:

December 2020
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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 → ∞.