36 citations · 71 across the 14 of their papers we have counts for
15 papers · 1 filter
Finite-time singularity formation for the heat flow of the -system
Yannick Sire, Juncheng Wei, Youquan Zheng +1
We construct the first example of finite time blow-up solutions for the heat flow of the -system, describing the evolution of surfaces with constant mean curvature \begin{equati…
Infinite time bubbling for the Yang-Mills heat flow on
Yannick Sire, Juncheng Wei, Youquan Zheng
We investigate the long time behaviour of the Yang-Mills heat flow on the bundle . Waldron \cite{Waldron2019} proved global existence and smoothness of th…
Extinction behaviour for the fast diffusion equations with critical exponent and Dirichlet boundary conditions
Yannick Sire, Juncheng Wei, Youquan Zheng
For a smooth bounded domain , , we consider the fast diffusion equation with critical sobolev exponent $$\frac{\partial w}{\partialτ} =Δw^{\frac{n-…
Singularity formation in the harmonic map flow with free boundary
Yannick Sire, Juncheng Wei, Youquan Zheng
In the past years, there has been a new light shed on the harmonic map problem with free boundary in view of its connection with nonlocal equations. Here we fully exploit this link…
Sign-changing blowing-up solutions for the critical nonlinear heat equation
Manuel del Pino, Monica Musso, Juncheng Wei +1
Let be a smooth bounded domain in and denote the regular part of the Green's function on with Dirichlet boundary condition as . Assume that …
Infinite time blow-up for the fractional heat equation with critical exponent
M. Musso, Y. Sire, J. Wei +2
We consider positive solutions for the fractional heat equation with critical exponent \begin{equation*} \begin{cases} u_t = -(-Δ)^{s}u + u^{\frac{n+2s}{n-2s}}\text{ in } Ω\times (…