9 papers
Classification of the dynamics of radial solutions to the 2D parabolic-elliptic Keller-Segel System
Federico Buseghin, Charles Collot
This note gives a complete classification of the asymptotic behavior of radial solutions to the two-dimensional parabolic-elliptic Keller-Segel system on the whole space, for gener…
Determination of the long-time dynamics for the 2D Keller-Segel equation at critical mass
Federico Buseghin, Charles Collot
We consider the parabolic-elliptic Keller-Segel equation in two dimensions on the whole space. We prove that for arbitrary initial data with critical mass and finite second mo…
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…
Strichartz estimates for a class of Schrödinger equations with a drift
Federico Buseghin, Nicola Garofalo
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schrödinger equations with a real drift.
Existence of finite time blow-up in Keller-Segel system
Federico Buseghin, Juan Davila, Manuel del Pino +1
Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system $\begin{equation} \begin{cases} u_{t} =Δu - \nabla \cdot(u \nabla v) \ \ \ \text{in } \mathbb{R…
A sub-Riemannian maximum modulus theorem
Federico Buseghin, Nicolò Forcillo, Nicola Garofalo
In this note we prove a sub-Riemannian maximum modulus theorem in a Carnot group. Using a nontrivial counterexample, we also show that such result is best possible, in the sense th…
The thin obstacle problem for some variable coefficient degenerate elliptic operators
Agnid Banerjee, Federico Buseghin, Nicola Garofalo
In this paper we establish the optimal interior regularity and the smoothness of the regular part of the free boundary in the thin obstacle problem for a class of degener…
On the limiting behaviour of some nonlocal seminorms: a new phenomenon
Federico Buseghin, Nicola Garofalo, Giulio Tralli
In this note we study the behaviour as of some semigroup based Besov seminorms associated with a non-symmetric and hypoelliptic diffusion with a drift. Our results gener…
A chain rule for a class of evolutive nonlocal hypoelliptic equations
Federico Buseghin, Nicola Garofalo
We prove a chain rule of local type for a class of fractional hypoelliptic equations of Kolmogorov-Fokker-Planck type. We introduce a semigroup based notion of nonlocal \emph{carré…