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Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane
In the present article we consider several issues concerning the doubly parabolic Keller-Segel system (1.1)-(1.2) in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, ...
On the Blow Up and Condensation of Supercritical Solutions of the Nordheim Equation for Bosons
In this paper we prove that the solutions of the isotropic, spatially homogeneous Nordheim equation for bosons with bounded initial data blow up in finite time in the L‚àû norm if the values of the energy and particle ...
Estimating the division rate of the growth-fragmentation equation with a self-similar kernel
We consider the growth-fragmentation equation and we address the problem of estimating the division rate from the stable size distribution of the population, which is easily measured, but non-smooth. We propose a method ...
Finite time blow-up and condensation for the bosonic Nordheim equation
The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the ...