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

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### 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

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### Decay and non-decay of the local energy for the wave equation in the De Sitter - Schwarzschild metric

... 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

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### DECAY OF LOCAL ENERGY FOR SOLUTIONS OF THE FREE SCHRÖDINGER EQUATION IN EXTERIOR DOMAINS

... 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

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### Exponential decay for the Schrödinger equation on a dissipative waveguide

... 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

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### CONCENTRATION OF LAPLACE EIGENFUNCTIONS AND STABILIZATION OF WEAKLY DAMPED WAVE EQUATION

... 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

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### Quasimodes and a lower bound for the local energy decay of the Dirac equation in Schwarzschild-Anti-de Sitter spacetime

... 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

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### Complexity and regularity of maximal energy domains for the wave equation with fixed initial data

... 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

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### Geometric control condition for the wave equation with a time-dependent observation domain

... 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

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### en fr Decay of semilinear damped wave equations: cases without geometric control condition Décroissance des équations des ondes amorties semilinéaires : des cas sans la condition de contrôle géométrique

... 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

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### EIGENMODES OF THE DAMPED WAVE EQUATION AND SMALL HYPERBOLIC SUBSETS

... 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

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### DECAY FOR THE KELVIN-VOIGT DAMPED WAVE EQUATION: PIECEWISE SMOOTH DAMPING

... 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

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### Decay rates for the damped wave equation on the torus

... 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

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### Exponential decay for the damped wave equation in unbounded domains

... 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

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### Dispersion for the wave equation outside a ball and counterexamples

... 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

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### A minimum effort optimal control problem for the wave equation.

... 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

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### Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation

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

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### Wave chaos for the Helmholtz equation

... 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

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### Time-Domain BEM for the Wave Equation on Distributed-Heterogenous Architectures : a Blocking Approach

... 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

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### Maximum Decay Rate for the Nonlinear Schrödinger Equation

... 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

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### Solutions of the time-harmonic wave equation in periodic waveguides : asymptotic behaviour and radiation condition

... 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

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