Related papers: Hypocoercivity for the non-linear semiconductor Bo…
We study the process of equilibration between two non-extensive subsystems in the framework of a particular non-extensive Boltzmann equation. We have found that even subsystems with different non-extensive properties achieve a common…
In this paper we study the pseudomonotone equilibrium problem. We consider a new inertial condition for the subgradient extragradient method with self-adaptive step size for approximating a solution of the equilibrium problem in a real…
We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field…
The non-equilibrium dynamics of electrons is of a great experimental and theoretical value providing important microscopic parameters of the Coulomb and electron-phonon interactions in metals and other cold plasmas. Because of the…
In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from the initial data and collision kernel is studied. Well-posedness and long-time behavior - exponential decay to the global equilibrium - of the…
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been…
This article is concerned with the Schauder estimate for linear kinetic Fokker-Planck equations with H\"older continuous coefficients. This equation has an hypoelliptic structure. As an application of this Schauder estimate, we prove the…
We propose a modified Boltzmann nonlinear electric-transport framework which differs from the nonlinear generalization of the linear Boltzmann formalism by a contribution that has no counterpart in linear response. This contribution follows…
We have combined the Boltzmann transport equation with an {\it ab initio} approach to compute the thermoelectric coefficients of semiconductors. Electron-phonon, ionized impurity, and electron-plasmon scattering rates have been taken into…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…
We study the non-equilibrium dynamics (purely dissipative and relaxational) in a semi-infinite system following a quench from the high temperature disordered phase to its critical temperature. We show that the local autocorrelation near the…
Motivated by the recently observed failure of the kinetic theory for the bulk viscosity, we in turn revisit the shear viscosity and the thermal conductivity of two-component fermions with a zero-range interaction both in two and three…
This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and…
We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To…
We are interested in the long-time behaviour of the kinetic Vicsek equation, rigorously derived as the mean-field limit~\cite{bolley2012meanfield} of a coupled system of~$N$ stochastic differential equations describing particles moving at…
For different models of the electron-phonon interaction, the asymptotic behaviour of the moments of the stationary homogeneous solution of the linear Boltzmann equation is determined in the limit of a high external field. For…
In this thesis, we consider the thin-film equation with nonlinear surface tension term in one space dimension. Relying on the corresponding energy and entropy estimates, we prove existence of weak solutions as well as nonnegativity results.