数学物理学报(英文版)
數學物理學報(英文版)
수학물이학보(영문판)
Acta Mathematica Scientia
2003年
3期
405-412
,共8页
Uniqueness%stationary solution%Euler-Poisson equation
In this paper,the uniqueness of stationary solutions with vacuum of EulerPoisson 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 the authors 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|θ and θ∈{0} ∪ [2(N - 2),+∞).
