On the Inhomogeneous System of Isentropic Gas Dynamics by Viscosity Method

Weifu Fang; Kazufumi Ito

doi:10.1017/S0308210500023647

On the Inhomogeneous System of Isentropic Gas Dynamics by Viscosity Method

Weifu Fang, Kazufumi Ito

Wright State University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
Volume	127
DOIs	https://doi.org/10.1017/S0308210500023647
State	Published - Jan 1 1997

Keywords

PDEs in connection with fluid mechanics
Partial differential equations
compressible fluids and gas dynamics
equations of meathmatical physics and other areas of application
generalized solutions
hyperbolic quations and systems
nonlinear first-order hyperbolic equations

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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.",

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AU - Ito, Kazufumi

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N2 - 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.

AB - 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.

KW - PDEs in connection with fluid mechanics

KW - Partial differential equations

KW - compressible fluids and gas dynamics

KW - equations of meathmatical physics and other areas of application

KW - generalized solutions

KW - hyperbolic quations and systems

KW - nonlinear first-order hyperbolic equations

UR - https://corescholar.libraries.wright.edu/math/448

U2 - 10.1017/S0308210500023647

DO - 10.1017/S0308210500023647

M3 - Article

VL - 127

JO - Proceedings of the Royal Society of Edinburgh. Section A. Mathematics

JF - Proceedings of the Royal Society of Edinburgh. Section A. Mathematics

ER -

On the Inhomogeneous System of Isentropic Gas Dynamics by Viscosity Method

Abstract

Keywords

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