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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...

Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields

Akira Iwatsuka, Hideo Tamura (1998)

Annales de l'institut Fourier

This article studies the asymptotic behavior of the number N ( λ ) of the negative eigenvalues < - λ as λ → + 0 of the two dimensional Pauli operators with electric potential V ( x ) decaying at ∞ and with nonconstant magnetic field b ( x ) , which is assumed to be bounded or to decay at ∞ . In particular, it is shown that N ( λ ) = ( 1 / 2 π ) ∫ V ( x ) > λ b ( x ) d x ( 1 + o ( 1 ) ) , when V ( x ) decays faster than b ( x ) under some additional conditions.

Asymptotic dynamics in double-diffusive convection

Mikołaj Piniewski (2008)

Applicationes Mathematicae

We consider the double-diffusive convection phenomenon and analyze the governing equations. A system of partial differential equations describing the convective flow arising when a layer of fluid with a dissolved solute is heated from below is considered. The problem is placed in a functional analytic setting in order to prove a theorem on existence, uniqueness and continuous dependence on initial data of weak solutions in the class ( [ 0 , ∞ ) ; H ) ∩ L ² l o c ( ℝ + ; V ) . This theorem enables us to show that the infinite-dimensional...

Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow

Gerhard Ströhmer (2008)

Studia Mathematica

We prove a priori estimates for a linear system of partial differential equations originating from the equations for the flow of a barotropic compressible viscous fluid under the influence of the gravity it generates. These estimates will be used in a forthcoming paper to prove the nonlinear stability of the motionless, spherically symmetric equilibrium states of barotropic, self-gravitating viscous fluids with respect to perturbations of zero total angular momentum. These equilibrium states as...

Asymptotic expansion in time of the Schrödinger group on conical manifolds

Xue Ping Wang (2006)

Annales de l’institut Fourier

For Schrödinger operator P on Riemannian manifolds with conical end, we study the contribution of zero energy resonant states to the singularity of the resolvent of P near zero. Long-time expansion of the Schrödinger group U ( t ) = e - i t P is obtained under a non-trapping condition at high energies.

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