Large-time behavior of the motion of a viscous heat-conducting one-dimensional gas coupled to radiation

2010 ◽  
Vol 191 (2) ◽  
pp. 219-260 ◽  
Author(s):  
Bernard Ducomet ◽  
Šárka Nečasová
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Heat Conducting ◽  
Time Behavior ◽  
One Dimensional ◽  
Viscous Heat

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

ASYMPTOTIC BEHAVIOR OF THE MOTION OF A VISCOUS HEAT-CONDUCTING ONE-DIMENSIONAL GAS WITH RADIATION: THE PURE SCATTERING CASE

2013 ◽  
Vol 11 (01) ◽  
pp. 1350003 ◽  
Author(s):  
BERNARD DUCOMET ◽  
ŠÁRKA NEČASOVÁ
Keyword(s):  
Large Time ◽  
Transport Coefficients ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Large Time Behavior ◽  
Heat Conducting ◽  
Time Behavior ◽  
Static State ◽  
Viscous Heat ◽  
Initial Boundary Value

We study the large-time behavior of the solution of an initial-boundary value problem for the equations of 1D motions of a compressible viscous heat-conducting gas coupled with radiation through a radiative transfer equation. Assuming only scattering processes between matter and photons (neglecting absorption and emission) and suitable hypotheses on the transport coefficients, we prove that the unique weak solution of the problem converges toward the static state.

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

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