Initial-boundary value problems for second order systems of
          partial differential equations∗

Heinz-Otto Kreiss; Omar E. Ortiz; N. Anders Petersson

Displaying similar documents to “Initial-boundary value problems for second order systems of partial differential equations∗”

Initial-boundary value problems for second order systems of partial differential equations

Heinz-Otto Kreiss, Omar E. Ortiz, N. Anders Petersson (2012)

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

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We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2 equations which leads to many complications, such as side conditions which must be satisfied by the solution of the larger...

Cramér type moderate deviations for Studentized U-statistics

Tze Leng Lai, Qi-Man Shao, Qiying Wang (2012)

ESAIM: Probability and Statistics

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Let be a Studentized U-statistic. It is proved that a Cramér type moderate deviation ( ≥ )/(1 − Φ()) → 1 holds uniformly in [0, ( )) when the kernel satisfies some regular conditions.

High-frequency limit of the Maxwell-Landau-Lifshitz equations in the diffractive optics regime

LU Yong (2012)

ESAIM: Proceedings

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We study the Maxwell-Landau-Lifshitz system for highly oscillating initial data, with characteristic frequencies (1 ) and amplitude (1), over long time intervals (1 ), in the limit → 0. We show that a nonlinear Schrödinger equation gives a good approximation for the envelope of the solution in the time interval under consideration. This extends previous results of Colin and Lannes [1]. This text is a short version of the article [5].