Asymptotic behavior of the solutions to a one-dimensional motion of compressible viscous fluids

Shigenori Yanagi

Mathematica Bohemica (1995)

  • Volume: 120, Issue: 4, page 431-443
  • ISSN: 0862-7959

Abstract

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We study the one-dimensional motion of the viscous gas represented by the system v t - u x = 0 , u t + p ( v ) x = μ ( u x / v ) x + f ∫ 0 x v x ¨ , t , 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.

How to cite

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Yanagi, Shigenori. "Asymptotic behavior of the solutions to a one-dimensional motion of compressible viscous fluids." Mathematica Bohemica 120.4 (1995): 431-443. <http://eudml.org/doc/247792>.

@article{Yanagi1995,
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\ddot\{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.},
author = {Yanagi, Shigenori},
journal = {Mathematica Bohemica},
keywords = {asymptotic behavior of solutions; one-dimensional motion of the viscous gas; compressible viscous gas; asymptotic behavior of solutions; one-dimensional motion of the viscous gas},
language = {eng},
number = {4},
pages = {431-443},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic behavior of the solutions to a one-dimensional motion of compressible viscous fluids},
url = {http://eudml.org/doc/247792},
volume = {120},
year = {1995},
}

TY - JOUR
AU - Yanagi, Shigenori
TI - Asymptotic behavior of the solutions to a one-dimensional motion of compressible viscous fluids
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 4
SP - 431
EP - 443
AB - 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\ddot{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.
LA - eng
KW - asymptotic behavior of solutions; one-dimensional motion of the viscous gas; compressible viscous gas; asymptotic behavior of solutions; one-dimensional motion of the viscous gas
UR - http://eudml.org/doc/247792
ER -

References

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