14 citations · 89 across the 19 of their papers we have counts for
3 papers · 1 filter
Existence and stability of infinite time blow-up in the Keller-Segel system
Juan Davila, Manuel del Pino, Jean Dolbeault +2
Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system \begin{equation}\tag{} \label{ks0} \left\{ \begin{aligned} u_t =&\; Δu - \nabla \cdot(u \…
Long-time asymptotics for evolutionary crystal dislocation models
Matteo Cozzi, Juan Dávila, Manuel del Pino
We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equation…
Blow-up for the 3-dimensional axially symmetric harmonic map flow into S2
Juan Davila, Manuel Del Pino, Catalina Pesce +1
We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere , \begin{align*} u_t & = Δu + |\nabla u|^2 u \quad \text{in } Ω\times(0,T) \\…