On the singular layer for the 1-D steady Euler system with heat conductivity in a finite nozzle as the heat conduction coefficient vanishes

Abstract: This paper investigates the singular limit problem of the one-dimensional steady compressible Euler system with heat conduction in a finite nozzle. The existence of the heat conduction solutions were established and boundary layers at one or two nozzle endpoints occur as the coefficient of heat conductivity goes to zero. The asymptotic behavior of the solutions vary depending on the state at the entrance and the value of the pressure at the exit, which classify the solutions into purely supersonic solution, purely subsonic solution and transonic solution. Moreover, we perform a formal asymptotic expansion of solutions and derive the boundary layer equations.