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Displaying 81 –
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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...
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....
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...
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.
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...
We consider a mesoscopic model for phase transitions in a periodic medium and we construct multibump solutions. The rational perturbative case is dealt with by explicit asymptotics.
We consider a mesoscopic model for phase transitions in a periodic medium
and we construct multibump solutions.
The rational perturbative case is dealt with by explicit
asymptotics.
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.
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.
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.
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 –
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