Acoustic wave propagation in anisotropic media with applications to piezoelectric materials. (English) Zbl 1525.35203
Summary: In this paper, we analyze acoustic wave propagation in anisotropic fluids and solids. By formulating the acoustic system as an evolution equation over a Hilbert space, we obtain global in time solutions when the associated material parameters are bounded and measurable. In particular, we prove well-posedness of a Cauchy problem for wave propagation in piezoelectric crystals. We then provide a stability analysis of these solutions not assuming positive definiteness of the stress-strain tensor or the piezoelectric stress tensor. Finally we prove continuous dependence on initial data, allowing the piezoelectric tensor to depend on space and time, provided solutions belong to an appropriate function space.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 76Q05 | Hydro- and aero-acoustics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74E10 | Anisotropy in solid mechanics |
| 74B05 | Classical linear elasticity |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35L90 | Abstract hyperbolic equations |
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 35R35 | Free boundary problems for PDEs |
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