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A note on poroacoustic traveling waves under Darcy’s law: exact solutions. (English) Zbl 1224.33014
Summary: A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy’s law, exact traveling wave solutions, as well as asymptotic or approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise and special or limiting cases are noted. Lastly, connections to other fields are pointed out and possible extensions of this work are briefly discussed.

MSC:
33E30 Other functions coming from differential, difference and integral equations
35L67 Shocks and singularities for hyperbolic equations
76N15 Gas dynamics (general theory)
76S05 Flows in porous media; filtration; seepage
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