共查询到20条相似文献,搜索用时 15 毫秒
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André Markoff 《Mathematische Annalen》1896,47(4):598-603
Sans résuméExtrait d'une lettre adressée à Mr. Klein 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(3):281-286
We prove an estimate for the Dirichlet-Neumann operator, and for the H1 local norm for solutions of Helmholtz equation outside an obstacle without trapping rays. We give an algorithm solving Helmholtz equation outside a union of such obstacles. Convergence follows from this estimate. At each step of the resolution, only one obstacle is considered for itself; this defines a decomposition domain technique fitting this equation. One can use different numerical schemes, one at each step, adapted to the considered component of the obstacle; therefore, this algorithm is a hybrid computation. The results are given for two obstacles, and the generalization is straightforward 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(3):221-226
We deal in this Note with the Laplace equation in the half-space. The use of a special family of weighted Sobolev spaces as a framework is at the heart of our approach. A complete class of existence, uniqueness and regularity results is obtained for inhomogeneous Dirichlet and Neumann problems. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(6):699-705
The aim of this work is to introduce and analyse the new algorithms for solving the transport equation in two-dimensional plane geometry. These schemes are based on a splitting method for the collision operator, introduced in [1]–[3]. Theoretical and numerical results are given and prove the superiority of these schemes over classical algorithms. 相似文献
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J. C. Nédélec 《Numerische Mathematik》1982,39(1):97-112
Summary We introduce some new families of finite element approximation for the stationary Stokes and Navier Stokes equations in a bounded domain in 3. These elements can used tetahedrons or cubes. The approximation satisfie exactly the incompressibility condition. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(11):987-991
We propose a notion of renormalized solutions for 3D Boltzmann equation, and without assuming Grad's angular cutoff. Actually, we show that P.-L. Lions's recent hypothesis about velocity averages compacity of solutions is satisfied in this framework. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(9):741-744
We announce several new theorems on the Diophantine equation (xn−1)/(x−1)=yq, which include the fact that any integer greater than 2 and with all digits equal to 1 in base ten cannot be a pure power. We then apply these results to solve this equation for any integer x of the form x=z1 with 2 ≤ z ≤ 10000 and t ≥ 1. 相似文献
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Résumé Dans une région des l'espace on considère l'écoulement d'un fluide et on fait l'hypothèse qu'il est pseudotridimensionnel, c'est-à-dire que son mouvement est stationnaire et qu'il existe un système de coordonnées curvilignes (y
1,y
2,y
3) tel que les surfaces coordonnéesy
3=constante sont des surfaces de courant. Cette hypothèse entraîne l'existence d'une fonction de courant (y
1,y
2,y
3). Si le fluide est parfait et barotrope on obtient que 3/ le long des lignes de courant oú 3 est la troisième composante contravariante du rotationnel de la vitesse et la densité de masse. Cette propriété permet de formuler une équation pour la fonction de courant, généralisant l'équation habituelle de la mécanique des fluides plans.
Let us consider a flow motion in a given special domain. We make the assumption that the movement of the fluid is pseudo-tridimensional, i.e., the flow motion is steady and there exists a system of curvilinear coordinates (y 1,y 2,y 3) such that stream surfaces are defined byy 3=constant. Under this assumption there exists a stream function .Whenever the fluid is perfect and barotropic, we show that 3/= constant on stream lines (where 3 is the 3rd contravariant component of the speed's curl and is the density).Using this property we are able to write an equation for the stream function, which embeds the usual equation for two-dimensional fluid movements.相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(12):1231-1236
We consider a conservative and entropie discrete-velocity model for the Bathnagar-Gross-Krook (BGK) equation. In this model, the approximation of the Maxwellian is based on a discrete entropy minimization principle. First, we prove a consistency result for this approximation. Then, we demonstrate that the discrete-velocity model possesses a unique solution. Finally, the model is written in a continuous equation form, and we prove the convergence of its solution toward a solution of the BGK equation. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(3):265-270
We prove the existence of weak solutions of the spatially homogeneous Boltzmann equation without angular cut-off assumption for inverse sth power molecules with s ≥ 7/3, and general initial data with bounded mass, kinetic energy and entropy. Next, we show the convergence of these solutions to solutions of the Landau-Fokker-Planck equation when the collision kernel concentrates around the value π/2 相似文献
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Torsten Carleman 《Acta Mathematica》1933,60(1):91-146
Sans résumé
Dédié àM. E. Holmgren à l'occasion de son soixantième anniversaire. 相似文献
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《Journal de Mathématiques Pures et Appliquées》2002,81(11):1113-1134
In odd dimension space, we prove, under a microlocal geometric condition, the exponential decay of the local energy for solutions of the wave equation on exterior domains, with Neumann damping ∂nu+a(x)∂tu=0. 相似文献