4 papers · 1 filter
On the Yamabe flow in a bounded domain
Fei Fang, Zhong Tan
This paper investigates the dynamical behaviors of solutions to the Yamabe flow via the modified potential well method. We first establish the local existence and regularity of wea…
Variational problems related to self-similar solutions of Hardy-Sobolev heat equation in RN
Fei Fang, Zhong Tan
In this paper, we apply a self-similar transformation to convert the parabolic equation with a Sobolev-Hardy term \begin{align*} u_t-Δu= \frac{|u|^{q-2}u}{\left|x\right|^s} & \text…
Global existence and blow-up for the Hardy-Sobolev parabolic equation in RN
Fei Fang, Zhong Tan
In this paper, we apply a self-similar transformation to convert the parabolic equation with a Hardy term \begin{equation*} \begin{cases}u_t-Δu-μ\frac{u}{|x|^2}=|u|^{2^*-2} u & \te…
Multiplicity of Positive Solutions of Nonlinear Elliptic Equation with Gradient Term
Fei Fang, Zhong Tan, Huiru Xiong
In this paper, we consider the following nonlinear elliptic equation with gradient term: \[ \left\{ \begin{gathered} - Δu - \frac{1}{2}(x \cdot \nabla u) + (λa(x)+b(x))u = βu^q +u^…