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Nicole Turbe, Louis Ratier (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We study the propagation of electromagnetic waves in a guide the section of which is a thin annulus. Owing to the presence of a small parameter, explicit approximations of the TM and TE eigenmodes are obtained. The cases of smooth and non smooth boundaries are presented.
Alinhac, Serge (1999)
Annals of Mathematics. Second Series
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J. Ralston (1978-1979)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Omel'yanov, G.A., Danilov, V.G., Radkevich, E.V. (1996)
Portugaliae Mathematica
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Stankovic, Bogoljub (1988)
International Journal of Mathematics and Mathematical Sciences
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Lassaad Aloui, Moez Khenissi (2007)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove uniform local energy estimates of solutions to the damped Schrödinger equation in exterior domains under the hypothesis of the Exterior Geometric Control. These estimates are derived from the resolvent properties.
Morris, Hedley C., Sheil, Derek, Dodd, Roger (1984)
International Journal of Mathematics and Mathematical Sciences
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Hu, Jinsong, Xu, Youcai, Hu, Bing (2010)
Boundary Value Problems [electronic only]
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Vladimir Kozlov, Vladimir Maz'ya (1999)
Journées équations aux dérivées partielles
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Asymptotic formulae for solutions to boundary value problems for linear and quasilinear elliptic equations and systems near a boundary point are discussed. The boundary is not necessarily smooth. The main ingredient of the proof is a spectral splitting and reduction of the original problem to a finite-dimensional dynamical system. The linear version of the corresponding abstract asymptotic theory is presented in our new book “Differential equations with operator coefficients”, Springer,...