References
- Ikeda T. Piezoelectricity. New York (New York): Oxford University Press; 1990.
- Dineva P, Gross D, Müller R. Dynamic fracture of piezoelectric materials. Vol. 10. Heidelberg, Germany: Springer; 2014.
- Knops RJ, Payne LE. Stability in linear elasticity. Int J Solids Struct. 1968;4(12):1233–1242. doi: https://doi.org/10.1016/0020-7683(68)90007-3
- Qi L. Eigenvalues of a real supersymmetric tensor. J Symb Comput. 2005;40(6):1302–1324. doi: https://doi.org/10.1016/j.jsc.2005.05.007
- Wilcox CH. Spectral and asymptotic analysis of acoustic wave propagation. In: Garnir HG, editor. Boundary value problems for linear evolution partial differential equations. D. Reidel Publishing Company; 1976. p. 385–473.
- Peng ZH, Zhang LS. A review of research progress in air-to-water sound transmission. Chinese Physics B. 2016;25(12):124306. doi: https://doi.org/10.1088/1674-1056/25/12/124306
- Leis R. Initial boundary value problems in mathematical physics. Chichester, UK: John Wiley & Sons; 1986.
- Reed M, Simon B. Methods of modern mathematical physics: vol. 2: fourier analysis, self-adjointness. Vol. 20, New York: Academic press; 1975.
- Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag; 1983.
- Wilcox C. Spectral analysis of the Pekeris operator in the theory of acoustic wave propagation in shallow water. Arch Ration Mech Anal. 1976;60(3):259–300. doi: https://doi.org/10.1007/BF01789259
- Brillouin L. Les tenseurs en mécanique et en élasticité. New York (New York): Masson; 1938.
- Levinshtein M, Shur MS, Rumyanstev S. Handbook series on semiconductor parameters. Vol. 1. Singapore: World Scientific; 1996.
- Wilcox CH. Initial-boundary value problems for linear hyperbolic partial differential equations of the second order. Arch Ration Mech Anal. 1962;10(1):361–400. doi: https://doi.org/10.1007/BF00281202
- Wilcox CH. The domain of dependence inequality for symmetric hyperbolic systems. Bulletin Amer Math Soc. 1964;70(1):149–155. doi: https://doi.org/10.1090/S0002-9904-1964-11056-9
- Sokolnikoff IS. Mathematical theory of elasticity. Vol. 83, New York: McGraw-Hill; 1956.
- Botkin N, Turova V. Simulation of acoustic wave propagation in anisotropic media using dynamic programming technique. 26th Conference on System Modeling and Optimization (CSMO); Berlin, Heidelberg: Springer; 2013. p. 36–51.
- Botkin ND, Hoffmann KH, Pykhteev OA, et al. Dispersion relations for acoustic waves in heterogeneous multi-layered structures contacting with fluids. J Franklin Inst. 2007;344(5):520–534. doi: https://doi.org/10.1016/j.jfranklin.2006.02.026
- Abo-el nour N, Askar NA. Calculation of bulk acoustic wave propagation velocities in trigonal piezoelectric smart materials. Applied Math & Information Sci. 2014;8(4):1625–1632. doi: https://doi.org/10.12785/amis/080417
- Reed M, Simon B. Methods of modern mathematical physics i: functional analysis. San Diego (California): Academic Press; 1980.
- Nagel R, Engel KJ. One-parameter semigroups for linear evolution equations. Vol. 194. New York (New York): Springer; 2000.
- Bloom F. Some stability theorems for an abstract equation in Hilbert space with applications to linear elastodynamics. J Math Anal Appl. 1977;61(2):521–536. doi: https://doi.org/10.1016/0022-247X(77)90135-4
- Barles G. Remarks on a flame propagation model. Valbonne, France: INRIA; 1985.
- Crandall MG, Lions PL. Viscosity solutions of Hamilton-Jacobi equations. Trans Am Math Soc. 1983;277(1):1–42. doi: https://doi.org/10.1090/S0002-9947-1983-0690039-8
- Hopf E. Generalized solutions of non-linear equations of first order. J Math Mech. 1965;14(6):951–973.
- Evans LC. Envelopes and nonconvex Hamilton–Jacobi equations. Calc Var Partial Differ Equ. 2014;50(1–2):257–282. doi: https://doi.org/10.1007/s00526-013-0635-3
- Stachura E. The time dependent Maxwell system with measurable coefficients in Lipschitz domains. J Math Anal Appl. 2017;452(2):941–956. doi: https://doi.org/10.1016/j.jmaa.2017.03.052