Showing papers in "Comptes Rendus Mathematique in 2007"

TL;DR: The method, based on an Offline–Online strategy relevant in the reduced basis many-query and real-time context, reduces the Online calculation to a small Linear Program: the objective is a parametric expansion of the underlying Rayleigh quotient; the constraints reflect stability information at optimally selected parameter points.

TL;DR: Ollivier et al. as discussed by the authors define a notion of Ricci curvature in metric spaces equipped with a measure or a random walk, which is compatible with Bakry-Emery theory and is robust and very easy to implement in concrete examples such as graphs.

TL;DR: Masmoudi et al. as discussed by the authors proved the global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model based on propagation of compactness.

TL;DR: Ern et al. as mentioned in this paper introduced a new H ( div ) flux reconstruction for discontinuous Galerkin approximations of elliptic problems, where the reconstructed flux is computed elementwise and its divergence equals the L 2 -orthogonal projection of the source term onto the discrete space.

TL;DR: Degond et al. as mentioned in this paper proposed a kinetic (mean-field) version of the Couzin-Vicsek algorithm and provided its formal macroscopic limit, which is based on the introduction of a nonconventional concept of a collisional invariant of the collision operator.

TL;DR: In this article, Savare et al. presented new results concerning wellposedness of gradient flows generated by λ-convex functionals in a wide class of metric spaces, including Alexandrov spaces satisfying a lower curvature bound and corresponding L 2 -Wasserstein spaces.

TL;DR: Farina et al. as discussed by the authors proved the non-existence of stable solutions for N ⩽ 9 in the two-dimensional case and demonstrated a classification theorem for solutions which are stable outside a compact set.

TL;DR: Blanchet et al. as discussed by the authors systematically studied weighted Poincare type inequalities which are closely connected with Hardy type inequalities and established the form of the optimal constants in some cases, such inequalities are then used to relate entropy with entropy production and get intermediate asymptotics results for fast diffusion equations.

TL;DR: In this paper, a new finite volume scheme was developed for the discretization of anisotropic diffusion problems, and the originality of this scheme lies in the fact that they were able to prove its convergence under very weak assumptions on the discreteization mesh.

TL;DR: In this paper, Dutykh et al. used the Helmholtz-Leray decomposition to model weakly dissipative free-surface flows using the classical potential flow approach.

TL;DR: Brugalle and Mikhalkin this paper compute enumerative invariants of real and complex projective spaces by means of some enriched graphs called floor diagrams, which they call floor diagrams.

TL;DR: Mihailescu et al. as discussed by the authors studied the nonlinear boundary value problem and proved several existence results in Sobolev spaces with variable exponents, where the continuous functions pi and q satisfy 2⩽pi(x) 1 for any x∈Ω¯ and any i∈{1,…,N}.

TL;DR: This work introduces the notion of an essential face, and the one of a core of a cell, and defines the critical kernel of a complex so that any complex which belongs to this class is homotopy equivalent to X.

TL;DR: In this article, Kukavica et al. proved the existence of strong solutions of the primitive equations for the ocean in space dimension 3 with the Dirichlet boundary condition, which can be easily adapted to treat full primitive equations in a domain with a varying bottom topography.

TL;DR: In this article, Allaire et al. studied the homogenization of a convection-diffusion equation with reaction in a porous medium when both the Peclet and Damkohler numbers are large.

TL;DR: BalBalaji et al. as mentioned in this paper proved that the Brauer group is Z / n Z, where n = g.c.d., and that Br (M ) is generated by the class of the projective bundle over M of relative dimension r − 1.

TL;DR: In this paper, the authors proposed a stabilized explicit coupling scheme for fluidstructure interaction based on Nitsche's method, which is stable irrespective of the fluidsolid density ratio.

TL;DR: In this paper, a travail presente les classes de conjugaisons des sous-groupe abeliens finis du groupe de Cremona du plan.

TL;DR: GroGrochenig and Lyubarskii as discussed by the authors derived sufficient conditions on the lattice Λ ⊆ R 2 such that the Gabor system { e 2 π i λ 2 t H n ( t − λ 1 ) : λ = (λ 1, λ2 ) ∈ Λ } is a frame.

TL;DR: Fan et al. as discussed by the authors proved that any p -adic transitive weak repeller is isometrically conjugate to a subshift of finite type where a suitable metric is defined.

TL;DR: Li et al. as discussed by the authors presented estimations asymptotiques du noyau de la chaleur sur les groupes de Heisenberg, and aussi les estimations optimales des derivees.

TL;DR: Ghergu et al. as discussed by the authors studied the existence or nonexistence of classical solutions to a singular Gierer-Meinhardt system with Dirichlet boundary condition, where the activator and the inhibitor have different sources given by general nonlinearities.

TL;DR: Zelenko and Li as discussed by the authors constructed a complete system of symplectic invariants for such parametrized curves, satisfying a certain genericity assumption, and give applications to geometric structures, including sub-Riemannian and sub-Finslerian structures.

TL;DR: In this paper, Friedland and Sodin demonstrate a simple analytic argument that may be used to bound the Levy concentration function of a sum of independent random variables, which is a version of a recent inequality due to Rudelson and Vershynin, and its multidimensional generalization.

TL;DR: Rozanova et al. as mentioned in this paper analyzed the derivation from Navier-Stokes system and the validity of its approximation, the existence, uniqueness and stability of the solution, and proved that the solution is global in time for sufficient small initial data with β > 0 and to have a blow-up if β = 0.

TL;DR: In this article, Boutet et al. considered the focusing nonlinear Schrodinger equation on the quarter plane and showed that the solution of the IBV problem has different asymptotic behaviors in different regions.

TL;DR: Ibrahim et al. as discussed by the authors extended the results of Lebeau and Christ to more general H 1 -supercritical nonlinearities and also extended those results to the 2D case for exponentially growing nonlinearity.

TL;DR: In this paper, a new construction relating formal groups, a class of Appell polynomials, and a family of Dirichlet L-series is proposed, where universal Bernoulli χ-numbers as well as generalized Riemann-Hurwitz zeta functions are introduced.

TL;DR: Petitta et al. as discussed by the authors showed that the duality solution of the associated elliptic problem is unique and converges to the Duality solution, which is the only solution that converges.

TL;DR: For example, Glade et al. as mentioned in this paper proposed a PH-decomposition for biological regulatory systems, which can be expressed as a set of equations combining a potential and a Hamiltonian part.