[PDF] Top 20 Energy decay for the damped wave equation under a pressure condition

... PRESSURE CONDITION EMMANUEL SCHENCK Abstract. We establish the presence of a spectral gap near the real axis for the damped wave equation on a ... Voir le document complet

... of the most efficient approaches to the question of local en- ergy decay is the theory of ...to the frequencies and rates of dumping of signals emitted by the black hole in ... Voir le document complet

... Since the early works of Lax and Phillips [18, 21] on exterior Dirichlet problem for the wave operator ∂ t 2 − ∆, it is well known that geometry of the boundary plays a crucial ... Voir le document complet

... that a weak assumption on the absorption index a (for instance the dissipation is effective on any open subset of the domain) is enough to ensure that the energy ... Voir le document complet

... as the damping b ≥ 0 is non trivial, the energy of every solution converge to 0 as t tends to ...On the other hand the rate of decay is uniform (and hence exponential) in ... Voir le document complet

... geodesic, a particle goes to timelike infinity in finite Boyer-Lindquist time (recall that along these geodesic, t − r ∗ and t + r ∗ are ...In the massless case, we would have to put boundary ...in ... Voir le document complet

... provide a complete mathematical analysis of the optimal design problem (P γ,T ...). The article is structured as ...give a sufficient condition ensuring the existence and ... Voir le document complet

... in a space-time domain, here (0, T ) × ...is the subject of the present article. The motivation for such a study can be seen as fairly ...contexts, for nondestructive ... Voir le document complet

... in the sense that there is an invariant compact set A ⊂ H 0 1 (Ω) ×L 2 (Ω), which consists of all the bounded trajectories and such that any regular set B bounded in (H 2 (Ω) ∩H 0 1 (Ω)) ×H 0 1 (Ω) ... Voir le document complet

... is a natural choice of Lagrangian states which is associated to the vertical bundle of the energy ...in a selfadjoint setting [1, 4] and also by Schenck in [28] in the context of ... Voir le document complet

... of the quasi-modes restricted to the interface by transmission ...prove the propagation theorem for the hyperbolic problem in Ω 2 which will lead to a ...to the elliptic ... Voir le document complet

... study the solutions of the quantization conditions ...account the relations (B.9) between the wavevectors k, k ′ and the energy ...describe the full spectrum (which we ... Voir le document complet

... and the integral term is compact since f is compactly supported in x and due to either the compact Sobolev embedding H 1 ,→ L 2p for p < d/(d − 2) or to more technical arguments based on ... Voir le document complet

... is the reflected wave: the phase has a singular, Airy type term (easy to deal ...hit the boundary without being deviated, only the diffracted wave part (containing I D ) ... Voir le document complet

... mizing the tracking error by means of a control which is pointwise as small as ...possible. The appearance of the L ∞ –control costs leads to ...nondifferentiability. The analytic and ... Voir le document complet

... Vi¸san. The focusing energy-critical nonlinear schr¨ odinger equation in dimen- sions five and ...regularity for semilinear wave ... Voir le document complet

... TIME-RESPONSE) A. Spectral Rigidity ` a la Berry (diagonal approximation) ...In a complex wave system, either a chaotic cavity or a disordered medium, it is not possible to give ... Voir le document complet

... on the Sparse Matrix-Vector product (SpMV) which has been widely studied on CPU and GPU because this is an essential operation in many scientific ap- ...improvement for the general SpMV on GPU ... Voir le document complet

... show the results of Section 2 , if we suppose a suitable asymptotic behavior of the initial value (u(0) ∈ X if α 6 N 4 , u(0) ∈ H 1 (R N ) if α > 4 N ), then we have a sharp lower ... Voir le document complet

... ing the whole space : this is the so called Sommerfeld radiation condition that represents the fact that, at infinity, the solution looks like an outgoing spheri- cal wave which ... Voir le document complet