K. M. Hui

collaborators

3 papers

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

Existence of new self-similar solutions of the fast diffusion equation

Kin Ming Hui

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

math.AP2024

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

Kin Ming Hui

Let $n \geq 3$ , $0 < m < \frac{n - 2}{n}$ , $I ¨ _{1} > 0$ , $I^\cdot > 0$ , $I^^{2} > \frac{m I ¨ _{1}}{n - 2 - nm}$ , $I^\pm = I^\pm_{m} = \frac{2 I ^ ^{2} + I ¨ _{1}}{1 - m}$ , $I^_{0}^{2} > 0$ and $I^\pm_{0} = 2 I^_{0}^{2} + 1$ . We use fixed point argument to give a n…