Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (3): 405-.

• Articles • Previous Articles     Next Articles

UNIQUENESS OF STATIONARY SOLUTIONS WITH VACUUM OF EULER-POISSON EQUATIONS

 DENG Yin-Bin, GUO Yu-Jin   

  1. Laboratory of Nonlinear Analysis, Department of Mathematics,
    Central China Normal University, Wuhan 430079, China
  • Online:2003-07-14 Published:2003-07-14
  • Supported by:

    Research was supported by the Natural Science Foundation of China and the
    Excellent Teachers Foundation of Ministry of Education of China.

Abstract:


\small\begin{quote}\bf Abstract\quad \rm In this paper, the
uniqueness of stationary solutions with vacuum of Euler-Poisson
equations is considered.
 Through a nonlinear transformation which is a function
of density and entropy, the corresponding problem can be reduced to
a semilinear elliptic equation with a nonlinear source term
consisting of  a power function, for which the classical
theory$^{[4],[9]}$
 of the elliptic equations leads us to the uniqueness result
under some assumptions on  the entropy function $S(x)$. As an
example, the authors  get the uniqueness of stationary solutions
with vacuum of Euler-Poisson equations for $S(x) = |x|^\theta $ and
$\theta \in \left \{0 \right \} \cup [2(N-2), +\infty)$.

Key words: Uniqueness, stationary solution, Euler-Poisson equation

CLC Number: 

  • 35J60
Trendmd