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Global stability to steady supersonic solutions of the 1-D compressible Euler equations with frictions. (English) Zbl 1462.35274

Summary: In this paper, using wave decomposition and establishing uniform a priori \(C^1\) estimates, we proved global stability of steady supersonic Fanno flows under small perturbations of initial-boundary values in a one-dimensional rectilinear finite duct with constant cross-sections. The flow is governed by the one-space dimensional compressible Euler equations with a nonlinear damping term representing frictions in the duct. Both isentropic and non-isentropic polytropic gases are considered.

MSC:

35Q31 Euler equations
76J20 Supersonic flows
76N06 Compressible Navier-Stokes equations
35B45 A priori estimates in context of PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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