一类非线性chemotaxis系统的局部零能控性

本文研究了一类非线性chemotaxis系统的能控性问题.利用这类线性化结合不动点的方法,获得了非线性系统的局部零能控性结果,推广了非线性抛物-椭圆型方程能控性的结果.     

可压缩欧拉-泊松方程组平衡解的存在性

可压缩欧拉-泊松方程组描述的是具自引力势能气态星体内部气体的运动变化.对于满足质量守恒和能量守恒的一些速度场,本文在熵函数的光滑性较弱的条件下研究欧拉-泊松方程组平衡解的存在性.在本文中,作者应用变分方法得到6/5＜γ＜2时方程组平衡解的存在性结果.该结果减弱了关于非旋转星体欧拉-泊松方程组平衡解存在的条件,从而适用于更一般的物理环境.     

A NOTE ON THE EXISTENCE OF STATIONARY SOLUTIONS OF THE COMPRESSIBLE 6 EULER-POISSON EQUATIONS WITH 5/6〈γ 〈 2

This paper is concerned with the system of Euler-Poisson equations as a model to describe the motion of the self-induced gravitational gaseous stars. When ~ 〈 7 〈 2, under the weak smoothness of entropy function, we find a sufficient condition to guarantee the existence of stationary solutions for some velocity fields and entropy function that solve the conservation of mass and energy.     

SOLUTIONS OF EULER-POISSON EQUATIONS IN R^n

In this article, the authors study the structure of the solutions for the EuierPoisson equations in a bounded domain of Rn with the given angular velocity and n is an odd number. For a ball domain and a constant angular velocity, both existence and nonexistence theorem are obtained depending on the adiabatic gas constant 7. In addition, they obtain the monotonicity of the radius of the star with both angular velocity and center density. They also prove that the radius of a rotating spherically symmetric star, with given constant angular velocity and constant entropy, is uniformly bounded independent of the central density. This is different to the case of the non-rotating star.