Long time approximations for solutions of wave equations via standing waves from quasimodes. (English) Zbl 1159.47057
The author deals with second-order evolution problems, providing estimates for the time, in which standing waves approach their solutions, when the initial data are connected with quasimodes of the associated positive, symmetric and compact operations on a Hilbert space. Asymptotics for low and high frequency vibrations in certain singularly perturbed spectral problems, which depend on a small parameter, are thus described. These results are applied to vibrating systems with concentrated masses; it is thus possible to detect standing waves affecting only certain regions.
Reviewer: Petre P. Teodorescu (Bucureşti)
MSC:
| 47N20 | Applications of operator theory to differential and integral equations |
| 46N20 | Applications of functional analysis to differential and integral equations |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
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