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Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

Asymptotic behaviour of the scattering phase for non-trapping obstacles

Veselin Petkov, Georgi Popov (1982)

Annales de l'institut Fourier

Let S ( λ ) be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle 𝒪 R n , n 3 with Dirichlet or Neumann boundary conditions on 𝒪 . The function s ( λ ) , called scattering phase, is determined from the equality e - 2 π i s ( λ ) = det S ( λ ) . We show that s ( λ ) has an asymptotic expansion s ( λ ) j = 0 c j λ n - j as λ + and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.

Asymptotic distribution of eigenfrequencies for damped wave equations

Johannes Sjöstrand (2000)

Journées équations aux dérivées partielles

Il est bien connu que les fréquences propres associées à un d'Alembertien amorti sont confinées dans une bande parallèle à l'axe réel. Nous rappelons l'asymptotique de Weyl pour la distribution des parties réelles des fréquences propres, nous montrons que «presque toutes» les fréquences propres appartiennent à une bande déterminée par la limite de Birkhoff du coefficient d'amortissement. Nous montrons aussi que certaines moyennes des parties imaginaires convergent vers la moyenne du coefficient...

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