We prove the convergence of the hydrostatic reconstruction scheme with kinetic numerical flux for the Saint Venant system with Lipschitz continuous topography. We use a recently derived fully discrete sharp entropy inequality with dissipation, that enables us to establish an estimate in the inverse of the square root of the space increment ∆x of th...
Let Ω B n be a a compact smooth domain in the Poincaré ball model of the Hyperbolic space B n , n ≥ 5. Let 0 n−2 n−4 n(n−4) 4 − γ , then the following Dirichlet boundary value problem: −∆ B n u − γV 2 u − λu = V 2 (s) |u| 2 (s)−2 u in Ω B n u = 0 on ∂Ω B n , has infinitely many solutions. Here −∆ B n is the Laplace-Beltrami operator associated wit...
This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions on domains beyond the Lipschitz class. If there is an associated bounded semigroup on Lp0 , then we prove that...
In this paper we consider solutions to the perturbed Maxwell's equations in R d , for d = 2, 3. For such solutions we provide a complete asymptotic expansions of the (geometric) perturbations resulting from the presence of diametrically small heterogeneity with parameters different from the background medium. Our derivation is rigorous and is based...
This work is devoted to an analytical description of the dynamics of the static/flowing interface in thin dry granular flows. Our starting point is the asymptotic model derived by Bouchut et al. (2016) from a free surface incompressible model with viscoplastic rheology including a Drucker-Prager yield stress.This asymptotic model is based on the th...
For the nonlinear Klein-Gordon equation in R 1+d , we prove the existence of multi-solitary waves made of any number N of decoupled bound states. This extends the work of C{\^o}te and Mu{\~n}oz (Forum Math. Sigma 2 (2014)) which was restricted to ground states, as were most previous similar results for other nonlinear dispersive and wave models.
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed number of point vortices appear in the small energy regime; the model allows for discontinuities, and the energy penalizes their length. The novel phenomenon here is tha...
In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the energy of a sound wave, we consider a frequency model (the Helmholtz equation) with a damping on the boundary. The damping on the boundary is firstly related with the damping in the volume, knowing the macroscopic parameters of a fixed porous medium....
We consider a class of one-dimensional nonselfadjoint semiclassical pseudo-differential operators, subject to small random perturbations, and study the statistical properties of their (discrete) spectra, in the semiclassical limit h → 0. We compare two types of random perturbation: a random potential vs. a random matrix. Hager and Sjöstrand had sho...
Let h : R → R+ be a lower semi-continuous subbadditive and even function such that h(0) = 0 and h(θ) ≥ α|θ| for some α > 0. The h-mass of a k-polyhedral chain P =∑j θjσj in R n (0 ≤ k ≤ n) is defined as M h (P) := j h(θj) H k (σj). If T = τ (M, θ, ξ) is a k-rectifiable chain, the definition extends to M h (T) := M h(θ) dH k. Given such a rectifiabl...
