**
MATHEMATICA BOHEMICA, Vol. 120, No. 4, pp. 431-443, 1995
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#
Asymptotic behavior of the solutions

to a one-dimensional motion

of compressible viscous fluids

##
Shigenori Yanagi

* Shigenori Yanagi*, Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790, Japan, e-mail: ` syanagi@dpcsipc.dpc.ehime-u.ac.jp`

**Abstract:** We study the one-dimensional motion of the viscous gas represented by the system $v_{t}-u_{x} = 0$, $ u_{t}+ p(v)_{x} = \mu(u_{x}/v)_{x} + f \left( \int_0^xv\dd x,t \right)$, with the initial and the boundary conditions $(v(x,0), u(x,0)) = (v_{0}(x), u_{0}(x))$, $u(0,t) = u(X,t) = 0$. We are concerned with the external forces, namely the function $f$, which do not become small for large time $t$. The main purpose is to show how the solution to this problem behaves around the stationary one, and the proof is based on an elementary $L^{2}$-energy method.

**Keywords:** compressible viscous gas, asymptotic behaviour of the solutions

**Classification (MSC91):** 35Q30, 76N10, 76N15

**Full text of the article:**

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