冷等离子体方程的内部自由边界问题

相对论冷等离子体方程在任意给定时间区间上存在光滑解的一个充分条件

A sufficient condition for the existence of smooth solutions of the relativistic cold plasma equations on any given time interval

针对一维相对论冷等离子体方程的 Cauchy 问题，提出解在任意给定时间区间上保持光滑的初始数据充分条件，并通过数值实验验证条件精度、分析奇点结构。

二维冷等离子体中混合共振的极限吸收原理

Limiting absorption principle for a hybrid resonance in a two-dimensional cold plasma

本文针对二维冷等离子体中混合共振的边值问题，通过加权Sobolev空间中的先验界证明极限吸收原理，并利用解的正则与奇异分解引入辐射条件，确立适定问题。

Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation

We study the Lie point symmetries and the similarity transformations for the partial differential equations of the nonlinear one-dimensional magnetohydrodynamic system with the Hall term known as HMHD system. For this 1+1 system of partial differential equations we find that is invariant under the action of a seventh dimensional Lie algebra. Furthermore, the one-dimensional optimal system is derived while the Lie invariants are applied for the derivation of similarity transformations. We present different kinds of oscillating solutions.

冷等离子体方程的最简单解：从流体动力学模型到动力学模型的性质变化

The simplest solutions of cold plasma equations: change in properties from a hydrodynamic to a kinetic model

本文研究单一空间变量下Landau冷等离子体从动力学模型向流体动力学模型的过渡，通过构建多速度矩链并逐步闭合，发现第二步闭合会显著改变空间仿射解和行波解的性质。

冷等离子体渐近模型的推导与适定性

Derivation and well-posedness for asymptotic models of cold plasmas

本文推导了三种新的渐近模型，用于描述无碰撞等离子体在磁场中的运动，其中一种是非线性非局部Boussinesq系统，另一种是非局部波动方程，并探讨了其适定性及波破散现象。

Linearised electrodynamics and stabilisation of a cold magnetised plasma

We consider a linearized Euler--Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. We present the derivation of the model, and we show its well-posedeness, its strong and polynomial stability under suitable and fairly general assumptions, its exponential stability in the same conditions as the Maxwell system, and finally its convergence to the time-harmonic regime. No homogeneity assumption is made, and the topological and geometrical assumptions on the domain are minimal. These results appear strongly linked to the spectral properties of various …

关于冷等离子体行波解的存在性

On the existence of traveling wave solutions for cold plasmas

本文利用分岔理论和微分系统轨道分析，结合线性化与数值计算，证明了磁场中无碰撞等离子体渐近模型的小振幅周期行波及多种单调与非单调行波解的存在性。

On the conditions for the breaking of oscillations in a cold plasma

The Cauchy problem for a quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For some simplified formulation of the problem, a criterion for the existence of a global in time solutions is obtained. For the original problem, a sufficient condition for the loss of smoothness is found, as well as a sufficient condition for the solution to remain smooth at least for time $ 2 π$. In addition, it is shown that in the general case, arbitrarily small perturbations of the trivial state lead to the formation o…

冷等离子体中磁流体波的奇点形成

Singularity formation of hydromagnetic waves in cold plasma

本文研究冷等离子体磁流体波模型的 $C^1$ 爆破问题，提出了导致光滑解在有限时间破裂的充分条件，并利用拉格朗日形式将奇点形成问题转化为求解二阶常微分方程的零点。