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On the inhomogeneous system of isentropic gas dynamics by the viscosity method

Published online by Cambridge University Press:  14 November 2011

Weifu Fang  and
Kazufumi Ito
Weifu Fang
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26506, U.S.A.
Kazufumi Ito
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, U.S.A.
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Abstract

The existence of global weak solutions is shown for the equations of isentropic gas dynamics with inhomogeneous terms by the viscosity method. A generalised version of the method of invariant regions is developed to obtain the uniform L∞ bounds of the viscosity solutions, and the method of compensated compactness is applied to show the existence of weak solutions as limits of the viscosity solutions. The lower positive bound for the density function is also obtained. As an example, a hydrodynamic model for semiconductors is analysed

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 2 , 1997 , pp. 261 - 280
Copyright
Copyright © Royal Society of Edinburgh 1997

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