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Influence of bottom topography on long water waves

Florent Chazel (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotic expansion of the involved Dirichlet-Neumann operator. Then, following the global strategy...

Ingham type theorems and applications to control theory

Claudio Baiocchi, Vilmos Komornik, Paola Loreti (1999)

Bollettino dell'Unione Matematica Italiana

Ingham [6] ha migliorato un risultato precedente di Wiener [23] sulle serie di Fourier non armoniche. Modificando la sua funzione di peso noi otteniamo risultati ottimali, migliorando precedenti teoremi di Kahane [9], Castro e Zuazua [3], Jaffard, Tucsnak e Zuazua [7] e di Ullrich [21]. Applichiamo poi questi risultati a problemi di osservabilità simultanea.

Initial boundary value problem for generalized Zakharov equations

Shujun You, Boling Guo, Xiaoqi Ning (2012)

Applications of Mathematics

This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in ( 2 + 1 ) dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.

Initial boundary value problems of the Degasperis-Procesi equation

Joachim Escher, Zhaoyang Yin (2008)

Banach Center Publications

We mainly study initial boundary value problems for the Degasperis-Procesi equation on the half line and on a compact interval. By the symmetry of the equation, we can convert these boundary value problems into Cauchy problems on the line and on the circle, respectively. Applying thus known results for the equation on the line and on the circle, we first obtain the local well-posedness of the initial boundary value problems. Then we present some blow-up and global existence results for strong solutions....

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

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 n equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2n equations which leads to many complications, such as side conditions which must be satisfied by the solution of the larger first order...

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

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 n equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2n equations which leads to many complications, such as side conditions which must...

Injections de Sobolev probabilistes et applications

Nicolas Burq, Gilles Lebeau (2013)

Annales scientifiques de l'École Normale Supérieure

On démontre dans cet article des versions probabilistes des injections de Sobolev sur une variété riemannienne compacte, ( M , g ) . Plus précisément on démontre que pour des mesures de probabilité naturelles sur l’espace L 2 ( M ) , presque toute fonction appartient à tous les espaces L p ( M ) , p < + . On donne ensuite des applications à l’étude des harmoniques sphériques sur la sphère 𝕊 d  : on démontre (encore pour des mesures de probabilité naturelles) que presque toute base hilbertienne de L 2 ( 𝕊 d ) formée d’harmoniques sphériques...

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