Related papers: Hypocoercivity for the non-linear semiconductor Bo…
We study the pointwise behavior of the linearized Boltzmann equation on torus for non-smooth initial perturbation. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the…
We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations.…
We establish existence with sharp rates of decay and distance from the Chapman--Enskog approximation of small-amplitude shock profiles of a class of semilinear relaxation systems including discrete velocity models obtained from Boltzmann…
We prove the well-posedness of the Cauchy problem on torus to an eletromagnetoelastic system. The physical model consists of three coupled partial differential equations, one of them is a hyperbolic equation describing the elastic medium…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
This work deals with the non-cutoff Boltzmann equation for all type of potentials, in both the torus $\mathbf{T}^3$ and in the whole space $\mathbf{R}^3$, under the incompressible Navier-Stokes scaling. We first establish the well-posedness…
In this article, we make a prima facie case that there could be distinct advantages to exploiting a new class of finite flux equilibrium solutions of the Quantum Boltzmann equation in semiconductor lasers.
The mobility of surface electrons localized over helium films underlying solid substrates has been evaluated by solving the Boltzmann equation in the time relaxation approximation and the force balance equation in which an effective…
A model kinetic equation is solved exactly for a special stationary state describing nonlinear Couette flow in a low density system of inelastic spheres. The hydrodynamic fields, heat and momentum fluxes, and the phase space distribution…
In this paper, we investigate the problems of Cauchy theory and exponential stability for the inhomogeneous Boltzmann equation without angular cut-off. We only deal with the physical case of hard potentials type interactions (with a…
In this work we present several quantitative results of convergence to equilibrium for the linear Boltzmann operator with soft potentials under Grad's angular cutoff assumption. This is done by an adaptation of the famous entropy method and…
The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of…
A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal…
In this paper we focus on different -- global, semi-local and local -- versions of Hoffman type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces and we…
We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a…
A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of…
In this paper, we study the spatially homogeneous inelastic Boltzmann equation for the angular cutoff pseudo-Maxwell molecules with an additional term of linear deformation. We establish the existence of non-Maxwellian self-similar profiles…
We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition…
We theoretically study the coherent nonlinear response of electrons confined in semiconductor quantum wells under the effect of an electromagnetic radiation close to resonance with an intersubband transition. Our approach is based on the…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…