Constitutive Relations for Monatomic Gases¶Based on a¶Generalized Rational Approximation¶to the Sum of the Chapman-Enskog Expansion |
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Authors: | Marshall Slemrod |
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Institution: | Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka 560‐0043, Japan, e‐mail: akitaka@math.sci.osaka‐u.ac.jp, JP Department of Computational Science, Faculty of Science, Kanazawa University, Kanazawa 920‐1192, Japan, e‐mail: mei@kappa.s.kanazawa‐u.ac.jp, JP
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Abstract: | . We study the asymptotic behavior as time goes to infinity of solutions to the initial‐boundary‐value problem on the half
space for a one‐dimensional model system for the isentropic flow of a compressible viscous gas, the so‐called p‐system with viscosity. As boundary conditions, we prescribe the constant state at infinity and require that the velocity
be zero at the boundary . When the velocity at infinity is negative and satisfies a condition on the magnitude, we prove that if the initial data
are suitably close to those for the corresponding outgoing viscous shock profile, which is suitably far from the boundary,
then a unique solution exists globally in time and tends toward the properly shifted viscous shock profile as the time goes
to infinity. The proof is given by an elementary energy method.
(Accepted March 2, 1998) |
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Keywords: | |
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