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On considère dans cet exposé le modèle asymptotique “shallow-water/shallow-water" obtenu dans [3] à partir du système d’Euler à deux couches avec fond plat et toit rigide pour décrire la propagation d’ondes internes de grande amplitude. En dimension d’espace un, ce système est de type hyperbolique et la théorie locale du problème de Cauchy ne pose pas de difficultés majeures, même si d’autres questions (explosion en temps fini, perte d’hyperbolicité) s’avèrent délicates. En dimension deux d’espace...
In this note we study the periodic homogenization problem for a particular bidimensional selfadjoint elliptic operator of the second order. Theoretical and numerical considerations allow us to conjecture explicit formulae for the coefficients of the homogenized operator.
We consider the problem of finding a couple of solutions satisfying the following conditions (4) and (5) for a couple of two uniformly elliptic partial differential operators and of order in a non regular situation.
We are interested in the theoretical study of a spectral problem
arising in a physical situation, namely interactions of fluid-solid
type structure. More precisely, we study the existence of solutions
for a quadratic eigenvalue problem, which describes the vibrations of a
system made up of two elastic bodies, where a slip is allowed on their
interface and which surround a cavity full of an inviscid
and slightly compressible fluid. The problem shall be treated like a
generalized eigenvalue...
The Navier–Stokes equations are approximated by means of
a fractional step, Chorin–Temam projection method; the time derivative
is approximated by a three-level backward finite difference, whereas
the approximation in space is performed by a Galerkin technique.
It is shown that the proposed scheme yields an error
of
for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is
the polynomial degree of the velocity approximation. It is also shown
that the splitting error of projection schemes based...
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