Construction de quasimodes de Rayleigh à grande durée de vie

For the Neumann problem in linear elasticity at the exterior of a convex body with analytic boundary in two dimension, we know that exists exactly two sequences of resonances z±k (called Rayleigh resonances), such that | z±k | e−C z±k . If the boundary is close enough to a circle and analytic in a wide enough complex band, we construct quasimodes associated to these resonances as far as possible from the obstacle. We study the exponential decay of these quasimodes according to the geometry of the obstacle. © 2006 Elsevier Inc. All rights reserved.