Kiss singularities of Green's functions of non-strictly hyperbolic equations

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 457, Issue 2009, 2001, Pages 1059-1077

  Borovikov, Vladimir A ^a   Gridin, Dmitri ^b  

^a BENEMÉRITA UNIVERSIDAD AUTÓNOMA DE PUEBLA   (Mexico)

^b School of Electrical   (United Kingdom)

Author keywords

Anisotropy; Green's function; Kiss singularity; Non strictly hyperbolic equations

Indexed keywords

EID: 57249083904     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0706     Document Type: Article

References (10)

1. Borovikov, V. A. 1959 Fundamental solutions of linear partial differential equations with constant coefficients. Trans. Moscow Math. Soc. 8, 199-257.
2. Borovikov, V. A. 2000 Singularities of the Green function for non-strictly hyperbolic operators. Russ. J. Math. Phys. 7, 261-278.
3. Burridge, R. 1967 The singularity on the plane lids of the wave surface of elastic media with cubic symmetry. Q. J. Mech. Appl. Math. 20, 41-56.
4. Courant, R. & Hilbert, D. 1962 Methods of mathematical physics, vol. II. New York: Interscience.
5. Fedoryuk, M. V. 1977 Saddle point method. Moscow: Nauka.
6. Gelfand, I. M. & Shilov, G. E. 1964 Generalized functions, vol. I. Academic.
7. Gridin, D. 2000 Far-field asymptotics of the Green's tensor for a transversely isotropic solid. Proc. R. Soc. Lond. A 456, 571-591.
8. Petrovski, I. G. 1945 On the diffusion of waves and lacunas for hyperbolic equations. Mat. Sbornik 17, 289-370.
9. Vavrycuk, V. 1999 Properties of S waves near a kiss singularity: a comparison of exact and ray solutions. Geophys. J. Int. 138, 581-589.
10. Wong, R. 1989 Asymptotic approximations of integrals. Academic.