双极流体动力学模型初边值问题解的整体存在性(英文)

Global existence of initial boundary problem solutions to bipolar hydrodynamical model

研究了1/4平面上的一维等熵双极流体动力学模型,这个模型是增加了电子场及由摩擦产生的阻尼的动量方程的Euler-Poisson系统,这类双极模型是目前研究较少的一类模型.通过引入合适的新的变量,将此方程转化为常见的阻尼波动方程,并在此基础上利用古典能量估计方法计算.应用分部积分以及边界估计的方法,证明了具有非零边界条件的初边值问题解的局部存在性.然后再利用标准的连续论断,将局部解扩展为整体解,最终证明了初边值问题古典解的整体存在性.

A model of one-dimensional isentropic bipolar hydrodynamical on the quarter plane R＋×R＋ is investigated,which makes the form of Euler-Poisson with the electric filed and frictional damping be added to the momentum equation,it is a less topic in bipolar model at present.Through introducing a new proper variation,the equation in the paper will be changed into a common damped wave equation,on this basis the local existence of the initial boundary value problem with non-zero boundary conditions is illustrated by using classical energy method integration by parts and boundary estimate via complicated calculation.Then,relying on the standard continuity argument,the local solution is extended to the global solution,and the global existence of classical solutions for the initial boundary value problem is proved at last.