相关论文: A degenerate fourth-order parabolic equation model…
A degenerate fourth-order parabolic equation modeling condensation phenomena related to Bose-Einstein particles is analyzed. The model is a Fokker-Planck-type approximation of the Boltzmann-Nordheim equation, only keeping the leading order…
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 existence of…
The paper is a continuation of our previous work on the spatially homogeneous Boltzmann equation for Bose-Einstein particles with quantum collision kernel that includes the hard sphere model. Solutions $F_t$ under consideration that…
Kaniadakis and Quarati (1994) proposed a Fokker--Planck equation with quadratic drift as a PDE model for the dynamics of bosons in the spatially homogeneous setting. It is an open question whether this equation has solutions exhibiting…
The Kompaneets equation describes a field of photons exchanging energy by Compton scattering with the free electrons of a homogeneous, isotropic, non-relativistic, thermal plasma. This paper strives to advance our understanding of how this…
Bose-Einstein condensation is usually modeled by nonlinear Schroedinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For…
In low-density or high-temperature plasmas, Compton scattering is the dominant process responsible for energy transport. Kompaneets in 1957 derived a non-linear degenerate parabolic equation for the photon energy distribution. In this paper…
This paper is devoted to the study of blow-up phenomenon for a fouth-order nonlocal parabolic equation with Neumann boundary condition, \begin{equation*} \left\{\begin{array}{ll}\ds u_{t}+u_{xxxx}=|u|^{p-1}u-\frac{1}{a}\int_{0}^a|u|^{p-1}u\…
In this paper, we study the initial value problem of a Boltzmann type equation with a nonlinear degenerate damping. We prove the existence of global weak solutions with large initial data, in three dimensional space. We rely on a variant…
We study the bosonic Boltzmann-Nordheim kinetic equation, which describes the kinetic regime of weakly interacting bosons with s-wave scattering only. We consider a spatially homogeneous fluid with an isotropic momentum distribution. The…
The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of…
We study a quantum Boltzmann-Condensation system that describes the evolution of the interaction between a well formed Bose-Einstein condensate and the quasi-particles cloud. The kinetic model is valid for a dilute regime at which the…
We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we prove existence and uniqueness for measure solutions.…
We study a nonlinear system coupling the Darcy-Forchheimer-Brinkman equations with a convection-diffusion-reaction equation, arising in reactive transport through porous media. The model features a nonlinear viscosity coupling, Forchheimer…
We consider effective models of condensation where the condensation occurs as time t goes to infinity. We provide natural conditions under which the build-up of the condensate occurs on a spatial scale of 1/t and has the universal form of a…
We review and extend the theory of the dynamics of Bose-Einstein condensation in weakly interacting atomic gases. We present in a unified way both the semiclassical theory as well as the full quantum theory. This is achieved by deriving a…
The Gross-Pitaevskii equation is a widely used model in physics, in particular in the context of Bose-Einstein condensates. However, it only takes into account local interactions between particles. This paper demonstrates the validity of…
In this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous Boltzmann equation for Bose-Einstein particles for the hard sphere model for bounded anisotropic initial data. The main idea of our…
A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and…
We consider an approximation of the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasiparticles in a dilute gas of bosons at low temperature. The corresponding collision frequency is neither…