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

Alexander Zlotnik and Mikhail Maksimov

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.