Diffusion électromagnétique à basse fréquence par un réseau de cylindres diélectriques. Étude numérique
Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model
Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous problem. Uniqueness...
Diffusive limit for finite velocity Boltzmann kinetic models.
We investigate, in the diffusive scaling, the limit to the macroscopic description of finite-velocity Boltzmann kinetic models, where the rate coefficient in front of the collision operator is assumed to be dependent of the mass density. It is shown that in the limit the flux vanishes, while the evolution of the mass density is governed by a nonlinear parabolic equation of porous medium type. In the last part of the paper we show that our method adapts to prove the so-called Rosseland approximation...
Dilogarithm identities for sine-Gordon and reduced sine-Gordon Y-systems.
Dimension reduction for functionals on solenoidal vector fields
We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint...
Dimension reduction for functionals on solenoidal vector fields
We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint...
Diophantine conditions in global well-posedness for coupled KdV-type systems.
Dirac equations with moving nuclei
Dirac fields on asymptotically flat space-times [Book]
Direct current electric potential in an anisotropic half-space with vertical contact containing a conductive 3D body.
Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method
In this paper, we study the boundary penalty method for optimal control of unsteady Navier–Stokes type system that has been proposed as an alternative for Dirichlet boundary control. Existence and uniqueness of solutions are demonstrated and existence of optimal control for a class of optimal control problems is established. The asymptotic behavior of solution, with respect to the penalty parameter ϵ, is studied. In particular, we prove convergence of solutions of penalized control problem to the...
Discontinuous Galerkin method for a 2D nonlocal flocking model
We present our work on the numerical solution of a continuum model of flocking dynamics in two spatial dimensions. The model consists of the compressible Euler equations with a nonlinear nonlocal term which requires special treatment. We use a semi-implicit discontinuous Galerkin scheme, which proves to be efficient enough to produce results in 2D in reasonable time. This work is a direct extension of the authors' previous work in 1D.
Discrete coagulation-fragmentation system with transport and diffusion
We prove the existence of solutions to two infinite systems of equations obtained by adding a transport term to the classical discrete coagulation-fragmentation system and in a second case by adding transport and spacial diffusion. In both case, the particles have the same velocity as the fluid and in the second case the diffusion coefficients are equal. First a truncated system in size is solved and after we pass to the limit by using compactness properties.
Discrete spectrum of the periodic elliptic operator with a differential perturbation
Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation.
Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications
2000 Mathematics Subject Classification: 35Q55,42B10.In this paper, we study the Schrödinger equation associated with the Dunkl operators, we study the dispersive phenomena and we prove the Strichartz estimates for this equation. Some applications are discussed.
Dispersion relations for the multivelocity acoustic Peierls equations and some properties of the scalar acoustic Peierls potential. I, II.
Dispersive waves and caustics.
Dissipation d’énergie pour des solutions faibles des équations d’Euler et Navier-Stokes incompressibles
On étudie l’équation locale de l’énergie pour des solutions faibles des équations d’Euler et Navier-Stokes incompressibles tridimensionnelles. On explicite un terme de dissipation provenant de l’éventuel défaut de régularité de la solution. On donne au passage une preuve simple de la conjecture d’Onsager, améliorant un peu l’hypothèse de [1]. On propose une notion de solution dissipative pour de telles solutions faibles.
Dissipative Boussinesq equations on non-cylindrical domains in .