相关论文: On shock waves from the inhomogeneous Boltzmann eq…
The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of…
We solve the continuation problem for the non-isentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar G\"uderley imploding shock solutions for a perfect gas with adiabatic…
We study a self-similar solution of the kinetic equation describing weak wave turbulence in Bose-Einstein condensates. This solution presumably corresponds to an asymptotic behavior of a spectrum evolving from a broad class of initial data,…
In this paper, we rigorously prove the existence of self-similar converging shock wave solutions for the non-isentropic Euler equations for $\gamma\in (1,3]$. These solutions are analytic away from the shock interface before collapse, and…
The Boltzmann H-theorem implies that the solution to the Boltzmann equation tends to an equilibrium, that is, a Maxwellian when time tends to infinity. This has been proved in varies settings when the initial energy is finite. However, when…
We study the structure of a shock wave for a two-, three- and four-component gas mixture on the basis of numerical solution of the Boltzmann equation for the model of hard sphere molecules. For the evaluation of collision integrals we use…
We investigate the nonequilibrium behavior of a one-dimensional binary fluid on the basis of Boltzmann equation, using an infinitely strong shock wave as probe. Density, velocity and temperature profiles are obtained as a function of the…
Self-similar solutions to converging (implosions) and diverging (explosions) shocks have been studied before, in planar, cylindrical or spherical symmetry. Here we offer a unified treatment of these apparently disconnected problems . We…
In this paper, we study the polyatomic Boltzmann equation based on continuous internal energy, focusing on physically relevant collision kernels of the hard potentials type with integrable angular part. We establish three main results:…
In this work, we analyze in detail the problem of piston driven shock waves in planar media. Similarity solutions to the compressible hydrodynamics equations are developed, for a strong shock wave, generated by a time dependent pressure…
This paper is concerned with the existence, shape and dynamical stability of infinite-energy equilibria for a general class of spatially homogeneous kinetic equations in space dimensions $d \geq 3$. Our results cover in particular…
This paper reviews results on the scalar Boltzmann equation for a single-component polyatomic gas with continuous internal energy. For the space homogeneous problem, $L^1$-theory is established, for solutions with initial strictly positive…
We consider a class of distribution functions having the form $ f(v,t)=t^{-dat} F(v e^{-at} )$, $ a=\mathrm{const.} $, where $ v $ and $ t $ denote the particle velocity and the time. This class of self-similar solutions to the spatially…
Plasma shock waves widely exist and play an important role in high-energy-density environment, especially in the inertial confinement fusion. Due to the large gradient of macroscopic physical quantities and the coupled thermal, electrical,…
Homo-energetic solutions to the spatially homogeneous Boltzmann equation have been extensively studied, but their global stability in the inhomogeneous setting remains challenging due to unbounded energy growth under self-similar scaling…
We derive and analyze shock-wave solutions of hydrodynamic equations describing repulsively interacting one dimensional Bose gas. We also use the number-conserving Bogolubov approach to verify accuracy of the Gross-Pitaevskii equation in…
The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations…
We study the structure, stability, and dynamics of dark solitary waves in parabolically trapped, collisionally inhomogeneous Bose-Einstein condensates (BECs) with spatially periodic variations of the scattering length. This collisional…
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…
We consider the spatially homogeneous Boltzmann equation for {\em inelastic hard spheres}, in the framework of so-called {\em constant normal restitution coefficients} $\alpha \in [0,1]$. In the physical regime of a small inelasticity (that…