ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY∗

doi:10.1007/s10473-023-0417-8

Abstract

Abstract: This paper is concerned with an ideal polytropic model of non-viscous and heat-conductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions. Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.

Key words: non-viscous, shock wave, outflow problem, boundary layer

Lili FAN, Meichen HOU. ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗[J].Acta mathematica scientia,Series B, 2023, 43(4): 1735-1766.

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ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗

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