Displaying similar documents to “On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations”

Estimates and computations for melting and solidification problems

James M. Greenberg (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we focus on melting and solidification processes described by phase-field models and obtain rigorous estimates for such processes. These estimates are derived in Section 2 and guarantee the convergence of solutions to non-constant equilibrium patterns. The most basic results conclude with the inequality (E2.31). The estimates in the remainder of Section 2 illustrate what obtains if the initial data is progressively more regular and may be omitted on first reading. We also...

Stabilization of second order evolution equations by a class of unbounded feedbacks

Kais Ammari, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain....

On a model of rotating superfluids

Sylvia Serfaty (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider an energy-functional describing rotating superfluids at a rotating velocity ω , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω , and the derivation of a limiting free-boundary problem.