39 citations · 217 across the 35 of their papers we have counts for
3 papers · 1 filter
Geometry driven Type II higher dimensional blow-up for the critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
We consider the problem v_t & = Δv+ |v|^{p-1}v \quad\hbox{in }\ Ω\times (0, T), v & =0 \quad\hbox{on } \partial Ω\times (0, T ) , v& >0 \quad\hbox{in }\ Ω\times (0, T) . In a domai…
Infinite time blow-up for the 3-dimensional energy critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
We construct globally defined in time, unbounded positive solutions to the energy-critical heat equation in dimension three $$ u_t = Δu + u^5 , \quad {\mbox {in}} \quad \R^3 \times…
Singularity formation for the two-dimensional harmonic map flow into
Juan Davila, Manuel del Pino, Juncheng Wei
We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere , \begin{align*} u_t & = Δu + |\nabla u|^2 u \quad \text{in } Ω\times(0,T) \\…