The inviscid limit of third-order linear and nonlinear acoustic equations. (English) Zbl 1475.35282
This work analyzes a model describing the evolution of sound waves through thermally relaxing media as the diffusivity of sound vanishes. The considered sound wave equation is third order in time and two kinds of nonlinearities, with different physical interpretations, are taken into account. The authors investigate the behavior of the solutions as the “diffisivity of sound” \(\delta\) vanishes. In other words, this paper deals with the vanishing sound diffusivity limit in thermally relaxing fluids or gases. It shows that sufficiently smooth solutions of these equations converge in the energy norm to the solutions of the corresponding inviscid models at a linear rate. The mathematical analysis is also complemented with numerical simulations.
Reviewer: Roberta Bianchini (Roma)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35L05 | Wave equation |
| 35L72 | Second-order quasilinear hyperbolic equations |
| 76Q05 | Hydro- and aero-acoustics |
| 76N15 | Gas dynamics (general theory) |
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