Abstract and Applied Analysis
Volume 2006 (2006), Article ID 69347, 12 pages
On symmetric equilibrium of an isothermal gas with a free boundary and a body force
Department of Mathematical Modelling, Moscow Power Engineering Institute, Krasnokazarmennaja 14, Moscow 111250, Russia
Received 16 December 2004; Accepted 20 February 2005
Copyright © 2006 Alexander Zlotnik and Mikhail Maksimov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The equation of symmetric equilibrium of an isothermal gas with an
unknown boundary in the field of a body force is considered.
Conditions for solvability and insolvability of the problem as
well as for uniqueness and nonuniqueness of solutions are
presented. Examples of finite, countable, or continual sets of
solutions are constructed including equipotential ones. Static
stability of solutions is analyzed too.