数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (3): 405-.
邓引斌, 郭玉劲
DENG Yin-Bin, GUO Yu-Jin
摘要:
\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
$\theta \in \left \{0 \right \} \cup [2(N-2), +\infty)$.
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