Steady Euler-Poisson Systems: A Differential/Integral
Equation Formulation with General Constitutive Relations
By: Joseph W. Jerome
The Cauchy problem and the initial-boundary value problem for the
Euler-Poisson system have been extensively investigated, together with a
study of scaled and unscaled asymptotic limits.
The pressure-density relationships
employed have included both the adiabatic (isentropic) relation
as well as the
ideal gas law (isothermal). The study most closely connected to this one
is that of S. Nishibata and M. Suzuki [Osaka J. Math. 44 (2007),
639--665], where a power law was employed in the context of the subsonic
case, covering both the isothermal and adiabatic cases. These authors
characterize the steady solution as an asymptotic limit. In this paper, we
consider only the steady case, in much greater generality, and with more
transparent arguments, than heretofore. We are able to identify both
subsonic and supersonic regimes, and correlate them to one-sided
boundary values
of the momentum and concentration.
We employ the novelty of a differential/integral equation formulation.
This paper has appeared electronically in Nonlinear Analysis:
vol. 71 (2009), pp. e2188--e2193.
doi: 10.1016/j.na.2009.04.042.