Stabilization of solutions of an exterior boundary value problem for some class of evolution systems

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1. [1] C. Bloom, A rate of approach to the steady state of solutions of second-order hyperbolic equation, J. Differential Equations 19 (1975), 296-329. Zbl0338.35060
2. [2] C. Bloom and H. Kazarinoff, Local energy decay for a class of nonstarshaped bodies, Arch. Rational Mech. Anal. 55 (1974), 73-85. Zbl0291.35053
3. [3] G. Dassios, Local energy decay for scattering of elastic waves, J. Differential Equations 49 (1983), 124-141. Zbl0476.35063
4. [4] B. V. Kapitonov, On the behavior, as t → ∞, of solutions of an exterior boundary value problem with the Leontovich condition for the Maxwell system, Soviet Math. Dokl. 37 (1988), 377-380. Zbl0694.35016
5. [5] B. V. Kapitonov, On exponential decay as t → ∞ of solutions of an exterior boundary value problem for the Maxwell system, Math. USSR-Sb. 66 (1990), 475-498. Zbl0706.35018
6. [6] B. V. Kapitonov, On the decay as t → ∞ of the solutions of the Cauchy problem for the Maxwell system in an inhomogeneous medium, in: Qualitative Analysis of Solutions of Partial Differential Equations, S. K. Godunov (ed.), Inst. Mat., Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk 1985, 100-109 (in Russian). 
7. [7] B. V. Kapitonov, On the decay of the solution of an exterior boundary value problem for the linear system of elasticity, Differentsial'nye Uravneniya 22 (1986), 452-458 (in Russian). 
8. [8] B. V. Kapitonov, Decay of solutions of an exterior boundary value problem and the principle of limiting amplitude for a hyperbolic system, Soviet Math. Dokl. 33 (1986), 243-247. Zbl0616.35051
9. [9] B. V. Kapitonov, Behavior as t → ∞ of the solutions of the exterior boundary-value problem for a hyperbolic system, Siberian Math. J. (1988), 444-457. Zbl0645.35059
10. [10] B. V. Kapitonov, On the decay as t → ∞ of solutions of an exterior boundary value problem for a strongly hyperbolic system, Soviet Math. Dokl. 41 (1990), 236-240. Zbl0724.35018
11. [11] B. V. Kapitonov, Stabilization of solutions and the principle of limiting absorption for a high order system, preprint 23, Inst. Mat., Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk 1989 (in Russian). 
12. [12] B. V. Kapitonov, Stabilization of solutions of mixed problems for a class of evolution systems, doctoral thesis, Novosibirsk 1990 (in Russian). 
13. [13] G. P. Menzala, Large time behavior of elastic waves in inhomogeneous medium, Boll. Un. Mat. Ital. B (7) 3 (1985), 95-108. Zbl0692.73022
14. [14] V. P. Mikhailov, On the principle of limiting amplitude, Dokl. Akad. Nauk SSSR 159 (1964), 750-752 (in Russian). 
15. [15] C. Morawetz, The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961), 561-568. Zbl0101.07701
16. [16] C. Morawetz, The limiting amplitude principle, ibid. 15 (1962), 349-361. Zbl0196.41202
17. [17] C. Morawetz, Energy decay for star-shaped obstacles, Appendix 3 to: P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, 1967, 261-264. 
18. [18] C. Morawetz, J. Ralston and W. Strauss, Decay of solutions of the wave equation outside nontrapping obstacles, Comm. Pure Appl. Math. 30 (1977), 447-508. Zbl0372.35008
19. [19] L. A. Muraveĭ, Asymptotic behaviour for large values of time of solutions of the second and third exterior boundary value problems for the wave equation with two space variables, Trudy Mat. Inst. Steklov. 126 (1973), 73-144 (in Russian). 
20. [20] L. A. Muraveĭ, On the asymptotic behaviour for large values of time of a solution of an exterior boundary value problem for the wave equation, Dokl. Akad. Nauk SSSR 220 (1975), 289-292 (in Russian). Zbl0318.35053
21. [21] W. Strauss, Dispersal of waves vanishing on the boundary of an exterior domain, Comm. Pure Appl. Math. 28 (1975), 265-278. Zbl0297.35047
22. [22] H. Tamura, On the decay of the local energy for wave equations with a moving obstacle, Nagoya Math. J. 71 (1978), 125-147. Zbl0405.35046
23. [23] H. Tamura, Local energy decays for wave equations with time-dependent coefficients, ibid. 107-123. Zbl0401.35064
24. [24] E. C. Zachmanoglou, The decay of solutions of the initial-boundary value problem for hyperbolic equations, J. Math. Anal. Appl. 13 (1966), 504-515. Zbl0135.31702