K. M. Hui

activity

20082025

most citedGlobal and touchdown behaviour of the generalized MEMS device equation

5 citations · 18 across the 25 of their papers we have counts for

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25 papers · 1 filter

math.AP2025

Asymptotic large time behavior of singular entire solutions of the fast diffusion equation

Kin Ming Hui, Jongmyeong Kim

Let $n \geq 3$ , $0 < m < \frac{n - 2}{n}$ , $α = \frac{2 β - 1}{1 - m}$ and $\frac{2}{1 - m} < \frac{α}{β} < \frac{n - 2}{m}$ . We give a new direct proof using fixed point method on the existence of singular…

math.AP2025

A matching construction of self-similar profiles for the fast diffusion equation

Kin Ming Hui

Let $n \geq 3$ , $0 < m < \frac{n - 2}{n}$ , $η > 0$ , $η_{0} > 0$ , $ρ_{1} > 0$ , $β_{-} (ρ_{1}) = - \frac{ρ _{1}}{2}$ , $β_{+} (ρ_{1}) = \frac{m ρ _{1}}{n - 2 - nm}$ and $α = \frac{2 β + ρ _{1}}{1 - m}$ . For any $β_{-} (ρ_{1}) \leq β \leq β_{+} (ρ_{1})$ ,…

math.AP2023

Existence and uniqueness of the singular self-similar solutions of the fast diffusion equation and logarithmic diffusion equation

Kin Ming Hui

Let $n \geq 3$ , $0 < m < \frac{n - 2}{n}$ , $ρ_{1} > 0$ , $η > 0$ , $β > \frac{m ρ _{1}}{n - 2 - nm}$ , $α = α_{m} = \frac{2 β + ρ _{1}}{1 - m}$ , $β_{0} > 0$ and $α_{0} = 2 β_{0} + 1$ . We use fixed point argument to give a new proof fo…

math.AP2022

Nonnegative solutions of the heat equation in a cylindrical domain and Widder's theorem

Kin Ming Hui, Kai-Seng Chou

It is shown every nonnegative solution of the heat equation in a bounded cylindrical domain has an integral representation in terms of a trace triple consisting of a bottom trace,…

math.AP2020

Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured Euclidean space

Kin Ming Hui, Jinwan Park

For $n \geq 3$ , $0 < m < \frac{n - 2}{n}$ , $β < 0$ and $α = \frac{2 β}{1 - m}$ , we prove the existence, uniqueness and asymptotics near the origin of the singular eternal self-similar solutions o…

math.AP2018

Vanishing time behavior of solutions to the fast diffusion equation

Kin Ming Hui, Soojung Kim

Let $n \geq 3$ , $0 < m < \frac{n - 2}{n}$ and $T > 0$ . We construct positive solutions to the fast diffusion equation $u_{t} = Δ u^{m}$ in $R^{n} \times (0, T)$ , which vanish at time $T$ . By…