Lower bound of the number of the Rayleigh resonances for arbitrary body

Indiana University Mathematics Journal

Volumn 49, Issue 1, 2000, Pages 405-426

  Stefanov, Plamen ^a  

^a EAST CAROLINA UNIVERSITY   (United States)

Author keywords

Rayligh waves; Resonances; Scattering poles

Indexed keywords

EID: 0000253768     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2000.49.1807     Document Type: Article

References (20)

1. F. CARDOSO & G. POPOV, Rayleigh quasimodes in linear elasticity, Comm. P.D.E., 17 (1992), 1327-1367.
2. F. CARDOSO & G. VODEV, Asymptotic behaviour of the scattering phase in linear elasticity for a strictly convex body, Comm. P.D.E., 22 (1997), 2025-2049.
3. _,Asymptotic behaviour of the scattering phase in linear elasticity II, Osaka J. Math., 35 (1998), 397-405.
4. C. GÉRARD, Asymptotique des poles de la matrice de scattering pour deux obstacles strictement convex, Bull. Soc. Math. France, Mémoire n. 31, 116, 1988.
5. M. KAWASHITA, On the local-energy decay property for the elastic wave equation with the Neumann boundary conditions, Duke Math. J., 67 (1992), 333-351.
6. _,On a region free from the poles of the resolvent and decay rate of the local energy for the elastic wave equation, Indiana Univ. Math. J., 43 (1994), 1013-1043.
7. G. NAKAMURA, Existence and propagation of Rayleigh waves and pulses, In: Modern Theory of Anisotropic Elasticity and Applications, (Research Triangle Park, NC, 1990), SIAM, Philadelphia, PA, 1991, pp. 215-231.
8. G. POPOV, Quasimodes for the Laplace operator and glancing hypersurfaces, In: Proceeding of Conference on Microlocal Analysis and Nonlinear Waves (M.Beals, R.Melrose, J.Rauch, eds), Minessota 1989, Springer 1991.
9. G. POPOV & G. VODEV, Resonances near the real axis for transparent obstacles, Comm. Math. Phys., to appear.
10. LORD RAYLEIGH, On waves propagated along plane surface of an elastic solid, Proc. London Math. Soc., 17 (1885), 4-11.
11. J. SJÖSTRAND & G. VODEV, Asymptotics of the number of Rayleigh resonances, Math. Ann., 309 (1997), 287-306.
12. J. SJÖSTRAND & M. ZWORSKI, Complex scaling and the distribution of scattering poles, Journal of AMS, 4 (1991), 729-769.
13. P. STEFANOV & G. VODEV, Distribution of resonances for the Neumann problem in linear elasticity outside a strictly convex body, Duke Math. J., 78 (1995), 577-714.
14. _,Neumann resonances in linear elasticity for an arbitrary body, Comm. Math. Phys., 176 (1996), 645-659.
15. P. STEFANOV, Quasimodes and resonances:sharp lower bounds, Duke Math. J., 99 (1999), 75-92.
16. S.-H. TANG & M. ZWORSKI, From quasimodes to resonances, Math. Res. Lett., 5 (1988), 261-272.
17. M. TAYLOR, Rayleigh waves in linear elasticity as a propagation of singularities phenomenon, In: Proc. Conf. on P.D.E. and Geometry, Marcel Dekker, New York, 1979, pp. 273-291.
18. _,Pseudodifferential Operators, Princeton University Press, Princeton, 1981.
19. G. VODEV, Existence of Rayleigh resonances exponentially close to the real axis, Ann. Inst. H. Poincaré (Phys. Théor.), 67 (1997), 41-57.
20. [Y] K. YAMAMOTO, Singularities of solutions to the boundary value problems for elastic and Maxwell's equations, Japan J. Math., 14 (1988), 119-163.