On the asymptotic behavior of the motion of a viscous, heat-conducting, one-dimensional real gas
We investigate the asymptotic behavior of smooth solutions as \(t \to \infty\) of initial boundary value problems for the equations of the one- dimensional motion of a viscous, heat-conducting, real gas. It is proved that solutions converge exponentially to a constant steady state for the confined gas, and in the free boundary case the volume occupied by the gas grows at least linearly in \(t\), while in the damped boundary case it grows more than logarithmically but not more than \(\sqrt t\). The proof is essentially based on a careful examination of a priori estimates which are shown to be independent of \(t\).
one-dimensional motion of a viscous, heat-conducting, real gas
scientific article; zbMATH DE number 704920
scientific article