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| LARGE-TIME BEHAVIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA |
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Citation： |
Xiao Ling(L. Hsiao),D. Serre.LARGE-TIME BEHAVIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA[J].Chinese Annals of Mathematics B,1995,16(4):433~446 |
| Page view： 1194
Net amount： 959 |
Authors： |
Xiao Ling(L. Hsiao); D. Serre |
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| Abstract： |
Consider the system
$$\cases v_t-u_x=0, \\ u_t+p(v, s)_x=-\al u,\ \ \al>0, \\ s_t=0, \endcases
\tag1$$
which can be used to model the adiabatic gas flow through porous media.
Here $v$ is specific volume, $u$ denotes velocity, $s$ stands for
entropy, $p$ denotes pressure with $p_v<0$ for $v>0$.
It is proved that the solutions of (1) tend to those of the
following nonlinear parabolic equation time-asymptotically:
$$
\cases v_t=-\frac1{\al}p(v, s)_{xx}, \\ s_t=0, \\ u=-\frac1{\al}p(v,
s)_x. \endcases |
Keywords： |
Large-time behavior, System of compressible adiabatic flow,Damping mechanism, Nonlinear parabolic equation. |
Classification： |
35K, 76S05 |
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