scholarly journals SUR LA STABILITÉ POUR L’ÉQUATION MONODIMENSIONNELLE D’UN GAZ VISQUEUX ET CALORIFÈRE AVEC LA FRONTIÈRE VARIABLE

2001 ◽  
Vol 44 (2) ◽  
pp. 295-315
Author(s):  
Rachid Benabidallah
Keyword(s):  
Boundary Conditions ◽  
Positive Constant ◽  
Large Time ◽  
Subject Classification ◽  
Heat Conducting ◽  
Time Behaviour ◽  
Initial Amplitude ◽  
Variable Boundary ◽  
One Dimensional ◽  
Viscous Heat

AbstractWe consider the equation of a one-dimensional viscous heat-conducting compressible gas in the variable domain with the appropriate boundary conditions. We study the large-time behaviour of the solution in the particular case where the displacement of the variable boundary is given by $L(t)=L_0(1+at)^\alpha$ with $0lt\alphalt1$, where $a$ is a positive constant and $L_0$ is the initial amplitude of our domain.AMS 2000 Mathematics subject classification: Primary 35B40; 76N15

Large-time behaviour of solutions for the outer pressure problem of a viscous heat-conductive one-dimensional real gas

1996 ◽  
Vol 126 (6) ◽  
pp. 1277-1296 ◽  
Author(s):  
L. Hsiao ◽  
T. Luo
Keyword(s):  
Asymptotic Behaviour ◽  
Large Time ◽  
Time Behaviour ◽  
Real Gas ◽  
Large Time Behaviour ◽  
One Dimensional ◽  
Viscous Heat

We investigate the large-time behaviour of solutions for the outer pressure problem of a viscous heat-conductive one-dimensional real gas. A conclusive answer to the problem of asymptotic behaviour is given in Theorem 1.2.

On the formation of weak plane shock waves by impulsive motion of a piston

1966 ◽  
Vol 25 (4) ◽  
pp. 705-718 ◽  
Author(s):  
John P. Moran ◽  
S. F. Shen
Keyword(s):  
Large Time ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Plane Shock ◽  
Heat Conducting ◽  
Piston Problem ◽  
Navier Stokes Equations ◽  
Viscous Heat ◽  
Equation Boundary ◽  
Weak Plane

The piston problem for a viscous heat-conducting gas is studied under the assumption that the piston Mach number ε is small. The linearized Navier–Stokes equations are found to be valid up to times of the order of ε−2mean free times after the piston is set in motion, while at large times the solution is governed by Burgers's equation. Boundary conditions for the large-time solution are supplied by the matching principle of the method of inner and outer expansions, which is also used to construct a composite solution valid both for small and for large times.

scholarly journals Decay rate of generalized solutions for equations of a viscous heat-conducting gas

2021 ◽  
Author(s):  
Zhilei Liang
Keyword(s):  
Large Time ◽  
Stokes Equations ◽  
Large Time Behavior ◽  
Ideal Gas ◽  
Generalized Solutions ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
Viscous Heat

The large time behavior is considered for the solutions of the Navier-Stokes equations for one-dimensional viscous polytropic ideal gas in unbounded domains. Using the local anti-derivatives functions technique, we obtain the power type decay estimates for the generalized solutions as time goes to infinity

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