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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...

Inverse du Laplacien discret dans le problème de Poisson-Dirichlet à deux dimensions sur un rectangle

Jean Chanzy (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Ce travail a pour objet l’étude d’une méthode de « discrétisation » du Laplacien dans le problème de Poisson à deux dimensions sur un rectangle, avec des conditions aux limites de Dirichlet. Nous approchons l’opérateur Laplacien par une matrice de Toeplitz à blocs, eux-mêmes de Toeplitz, et nous établissons une formule donnant les blocs de l’inverse de cette matrice. Nous donnons ensuite un développement asymptotique de la trace de la matrice inverse, et du déterminant de la matrice de Toeplitz....

Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains

M. Bochniak, Anna-Margarete Sändig (1999)

Mathematica Bohemica

We consider a class of semilinear elliptic problems in two- and three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Frechet differentiable. Applying the local invertibility theorem we prove that the solution of the semilinear problem has the same asymptotic...

Long-time asymptotics of solutions to some nonlinear wave equations

Grzegorz Karch (2000)

Banach Center Publications

In this paper, we survey some recent results on the asymptotic behavior, as time tends to infinity, of solutions to the Cauchy problems for the generalized Korteweg-de Vries-Burgers equation and the generalized Benjamin-Bona-Mahony-Burgers equation. The main results give higher-order terms of the asymptotic expansion of solutions.

Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates

Patrick Joly, Sébastien Tordeux (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between...

Nonlinear Pulse Propagation

Jeffrey Rauch (2001)

Journées équations aux dérivées partielles

This talk gives a brief review of some recent progress in the asymptotic analysis of short pulse solutions of nonlinear hyperbolic partial differential equations. This includes descriptions on the scales of geometric optics and diffractive geometric optics, and also studies of special situations where pulses passing through focal points can be analysed.

Numerical study of acoustic multiperforated plates

Abderrahmane Bendali, M’Barek Fares, Sophie Laurens, Sébastien Tordeux (2012)

ESAIM: Proceedings

It is rather classical to model multiperforated plates by approximate impedance boundary conditions. In this article we would like to compare an instance of such boundary conditions obtained through a matched asymptotic expansions technique to direct numerical computations based on a boundary element formulation in the case of linear acoustic.

On a fourth order equation in 3-D

Xingwang Xu, Paul C. Yang (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

On a Fourth Order Equation in 3-D

Xingwang Xu, Paul C. Yang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

Currently displaying 81 – 100 of 211