https://neckpinch.com/authors/nguyen-ngoc-khanh/New arXiv papers by Nguyen Ngoc Khanh, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1803.07251/arxiv:1803.07251Tue, 20 Mar 2018 00:00:00 GMTNguyen Thac Dung, Nguyen Ngoc Khanh — In this paper, we will address to the following parabolic equation uₜ=Δ_fu + F(u) on a smooth metric measure space with Bakry-Émery curvature bounded from below. Here F is a differentiable function defined in ℝ. Our motivation is originally inspired by gradient estimates of Allen-Cahn and Fisher equations (). In this paper, we show new gradient estimates for these equations. As their applications, we obtain Liouville type theorems for positive or bounded solutions to the above equation when either F=cu(1-u) (the Fisher equation) or; F=−u³+u (the Allen-Cahn equation); or F=aulog u (the equation involving gradient Ricci solitons).Ricci solitonsLimit spaces & RCDPhase fields & multiphase flows