| 概要 |
In the present talk, we discuss a large time behavior of a solution to a
coupled system of viscous and inviscid conservation laws. Mainly, we talk
about an asymptotic stability of a rarefaction wave, with assuming an
existence
of an entropy function. This condition enables us to transform the
original system
to a normal symmetric system, which is a coupled system of hyperbolic
and parabolic equations.
In asymptotic analysis, we derive an a priori estimate by an energy
method. Especially in deriving
the basic estimate, we make use of an energy form, which is defined by
substituting a smoothed
rarefaction wave in the entropy function. The symmetric system is
utilized in deriving higher
order estimates of the derivatives of solutions. In this procedure, we
have to suppose
that the stability condition hold at spatial far field.
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