9 citations · 21 across the 10 of their papers we have counts for
10 papers
Co-existence of Type II blow-ups with multiple blow-up rates for five-dimensional heat equation with critical nonlinear boundary conditions
Juncheng Wei, Zikai Ye, Xiaoyu Zeng +1
We consider the following five-dimensional heat equation with critical boundary condition \begin{equation*} \partial_t u=Δu \mbox{ \ in \ } \mathbb{R}_+^5\times (0,T) , \quad -\par…
Long-time dynamics for the energy critical heat equation in
Zaizheng Li, Qidi Zhang, Yifu Zhou +1
We investigate the long-time behavior of global solutions to the energy critical heat equation in \begin{equation*} \begin{cases} \pp_t u=Δu+|u|^{\frac{4}{3}} u ~&\mbox{ in }…
Trichotomy dynamics of the 1-equivariant harmonic map flow
Juncheng Wei, Qidi Zhang, Yifu Zhou
For the 1-equivariant harmonic map flow from into \begin{equation*} \left\{ \begin{aligned} &v_t=v_{rr}+\frac{v_r}{r} - \frac{\sin(2v)}{2r^2} , ~\quad(r,t)\in R_+\time…
On Fila-King Conjecture in Dimension Four
Juncheng Wei, Qidi Zhang, Yifu Zhou
We consider the following Cauchy problem for the four-dimensional energy critical heat equation \begin{equation*} \begin{cases} u_t=Δu+u^{3} ~&\mbox{ in }~ {\mathbb R}^4 \times (0,…
Finite-time singularity formations for the Landau-Lifshitz-Gilbert equation in dimension two
Juncheng Wei, Qidi Zhang, Yifu Zhou
We construct finite time blow-up solutions to the Landau-Lifshitz-Gilbert equation (LLG) from into \begin{equation*} \begin{cases} u_t= a(Δu+|\nabla u|^2u) -b…
Bubble towers in the ancient solution of energy-critical heat equation
Liming Sun, Juncheng Wei, Qidi Zhang
We construct a radially smooth positive ancient solution for energy critical semi-linear heat equation in , . It blows up at the origin with the profile of m…