14 citations · 89 across the 19 of their papers we have counts for
20 papers
Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system
Federico Buseghin, Juan Dávila, Manuel del Pino +1
We construct axially symmetric finite-time blow-up solutions to the three-dimensional Keller-Segel system. By adapting gluing techniques, we derive a precise asymptotic expansion f…
Delaunay-like compact equilibria in the liquid drop model
Manuel del Pino, Monica Musso, Andrés Zúñiga
The liquid drop model was introduced by Gamow in 1928 and Bohr-Wheeler in 1938 to model atomic nuclei. The model describes the competition between the surface tension, which keeps…
Interacting helical traveling waves for the Gross-Pitaevskii equation
Juan Dávila, Manuel del Pino, María Medina +1
We consider the 3D Gross-Pitaevskii equation \begin{equation}\nonumber i\partial_t ψ+Δψ+(1-|ψ|^2)ψ=0 \text{ for } ψ:\mathbb{R}\times \mathbb{R}^3 \rightarrow \mathbb{C} \end{equati…
New type II Finite time blow-up for the energy supercritical heat equation
Manuel del Pino, Chen-Chih Lai, Monica Musso +2
We consider the energy supercritical heat equation with the -th Sobolev exponent \begin{equation*} \begin{cases} u_t=Δu+u^{3},~&\mbox{ in } Ω\times (0,T),\\ u(x,t)=u|_{\part…
Type II Finite time blow-up for the three dimensional energy critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei +2
We consider the following Cauchy problem for three dimensional energy critical heat equation \begin{equation*} \begin{cases} u_t=Δu+u^{5},~&\mbox{ in } \ {\mathbb R}^3 \times (0,T)…
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 \…