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Large-time behavior of solutions to the inflow problem of full compressibleNavier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$.The wave structure which contains four waves: the transonic(or degenerate)boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and3-rarefaction wave to the inflow problem is described and the asymptoticstability of the superposition of the above four wave patterns to the inflowproblem of full compressible Navier-Stokes equations is proven under somesmallness conditions. The proof is given by the elementary energy analysisbased on the underlying wave structure. The main points in the proof are thedegeneracies of the transonic boundary layer solution and the wave interactionsin the superposition wave.

Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations