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Now showing items 1-10 of 10

#### Time asymptotics for a critical case in fragmentation and growth-fragmentation equations

(2016-01-01)

Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to the description of the long-time asymptotics of two critical cases of these equations, ...

#### Finite time blow-up for the bosonic Nordheim equation

(2015-12-31)

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 ...

#### Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature

(2015-09-01)

We consider an approximation of the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasipar-ticles in a dilute gas of bosons at low temperature. The corresponding collision ...

#### Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane

(2014-12-31)

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

(2014-12-31)

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

(2014-12-31)

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

(2014-12-31)

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 ...

#### Propagation of chaos in a coagulation model

(2013-12-31)

The dynamics of a finite system of coalescing particles in a finite volume is considered. It is shown that, in the thermodynamic limit, a coagulation equation is recovered and propagation of chaos holds for all time.

#### Blowup for a time-oscillating nonlinear heat equation

(2013-12-31)

In this paper, we study a nonlinear heat equation with a periodic time oscillating term in factor of the nonlinearity. In particular, we give examples showing how the behavior of the solution can drastically change according ...

#### Classical non-mass-preserving solutions of coagulation equations

(2012-12-31)

In this paper we construct classical solutions of a family of coagulation equations with homogeneous kernels that exhibit the behaviour known as gelation. This behaviour consists in the loss of mass due to the fact that ...