Global existence and asymptotic behavior for a viscous, heat-conductive, one-dimensinal real gas with fixed and thermally insulated endpoints (Q5937335)

One-dimensional viscous gas heat-conductive equations in the Lagrangian setting are considered in a bounded domain. The global unique existence is proved for the initial-boundary value problem with the no-slip and heat-insulated boundary conditions. Internal energy, pressure, heat conductivity and viscosity are given functions of temperature and specific volume. A number of restrictions for these functions are imposed. Particularly, it is prohibited that viscosity depends on temperature. The stability of solutions is proved as times goes to infinity.