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

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

**for**a

**wave**

**equation**

**damped**on a (small) part of

**the**...paper,

**the**authors also make

**the**following comment about

**the**result they obtain: “Notons toutefois ...

49

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

**the**uniform positivity of hγi T (x, ξ) in Σ

**for**some T > 0 implies that

**the**exponential

**decay**...in

**the**celebrated articles [30], [3] and [4] of Bardos, Lebeau, Rauch and ...

26

### Energy decay for the damped wave equation under a pressure condition

**the**presence of a spectral gap near

**the**real axis

**for**

**the**

**damped**

**wave**

**equation**on a manifold with negative ...by

**the**negativity of a topological pressure ...

33

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

**the**exponential stabilization, which holds

**for**

**the**

**wave**

**equation**with localized viscous damping a(x)∂ t u (see [ LR05 , Zh18 ]

**for**results using

**the**multiplier ...

34

### One-dimensional wave equation with set-valued boundary damping: well-posedness, asymptotic stability, and decay rates

**the**full X 2 by a density argument, ...to

**the**damping one ...2

**for**every s ∈ R), and exponential stability is achieved, ...−µt

**for**some positive constants C, µ, cf. [27]

**for**...

70

### QUANTITATIVE RATES OF CONVERGENCE TO EQUILIBRIUM FOR THE DEGENERATE LINEAR BOLTZMANN EQUATION ON THE TORUS

**equation**related to ( 1 ),

**the**1d Goldstein-Taylor type model, has been studied in [ 7 ] where

**the**authors do get explicit

**rates**via comparing this

**equation**to a

**damped**...

23

### Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation

**the**Kirchhoff

**equation**subject to a frictional damping, in contrast, there is just a few number of papers concerned with

**the**Kirchhoff

**equation**subject to a dissipation given by a ...

24

### Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation

**the**Kirchhoff

**equation**subject to a frictional damping, in contrast, there is just a few number of papers concerned with

**the**Kirchhoff

**equation**subject to a dissipation given by a ...

24

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

**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 ...

23

### Quantitative rates of convergence to equilibrium for the degenreate linear Boltzman equation on the Torus

**equation**related to ( 1 ),

**the**1d Goldstein-Taylor type model, has been studied in [7] where

**the**authors do get explicit

**rates**via comparing this

**equation**to a

**damped**...

22

### Stabilisation of wave equations on the torus with rough dampings

**the**works by Laurent [ 30 , 31 ], Kashiwara-Kawai [ 28 ], Sjöstrand [ 47 ], Lebeau [ 33 ] in

**the**analytic context, (see also Bony-Lerner [ 7 ] in

**the**C ∞ framework and Sjöstrand-Zworski [ 49 ] ...

30

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

**For**

**the**dissipative equations, this non-trapping assumption can be replaced by

**the**same damping condition (geometric control condition) on bounded trajectories as in

**the**compact case (where ...

22

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

**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 energy space ...

25

### NULL CONTROLLABILITY OF THE STRUCTURALLY DAMPED WAVE EQUATION ON THE TWO-DIMENSIONAL TORUS

**the**observability inequality ( ...estimates

**for**

**the**backward heat

**equation**( 1.34 ) and

**for**

**the**transport

**equation**( ...with

**the**same weights functions. ...

31

### Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

**the**existence of a spectral gap was established

**for**all α 6= α ∗ = (2 − d)/2, but its value was not stated

**for**all values of ...linearized

**the**fast diffusion flow (considered as a ...

7

### Global infinite energy solutions for the cubic wave equation

**the**case d = 4 one may expect to get uniqueness by combining

**the**analysis of [8] with

**the**critical H 1 theory

**for**...include

**the**case s = 0 by elaborating on

**the**arguments ...

13

### 1-D non-periodic homogenization for the seismic wave equation

**the**static case, this kind of problem has been studied

**for**a long time and a large number of results have been obtained us- ing

**the**so-called homogenization theory applied to media showing rapid ...

15

### Decay rates for radiative transitions in the Pr IV spectrum

**The**ground state of Pr IV is [Xe]4f 2 3 H 4 . All of

**the**term energies experimentally deduced so far are listed in

**the**NIST compilation (Martin et al 1978 ) which contains 88 levels identified as ...

12

### Alfvén Wave Propagation in the Io Plasma Torus

**the**Io

**torus**is close to rotating with Jupiter's 10 ‐hr spin ...that

**the**sulfur and oxygen ions experience a considerable centrifugal force that tends to con ﬁne them to

**the**farthest point ...

8

### Unique continuation property and control for the Benjamin-Bona-Mahony equation on the torus

**the**trivial one u ≡ ...to

**the**approximate controllability

**for**linear PDE, and it is involved in

**the**classical unique- ness/compactness approach in

**the**proof of

**the**stability ...

36