Bound state solutions for a class of nonlinear Schrödinger equations.
Bound states and scattering states for time periodic hamiltonians
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations.
Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations
Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations
Non reflecting boundary conditions on artificial frontiers of the domain are proposed for both incompressible and compressible Navier-Stokes equations. For incompressible flows, the boundary conditions lead to a well-posed problem, convey properly the vortices without any reflections on the artificial limits and allow to compute turbulent flows at high Reynolds numbers. For compressible flows, the boundary conditions convey properly the vortices without any reflections on the artificial limits...
Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded, for which the worst-case in terms of recirculation effects is inferred to correspond to a strong orifice flow through near-complete occlusion.A worst-case optimal control approach is applied to the steady Navier-Stokes...
Boundary control of the Maxwell dynamical system : lack of controllability by topological reasons
Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons
The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domain Ω ⊂ R3. Let ΩT ⊂ Ω be the subdomain filled by waves at the moment T, T* the moment at which the waves fill the whole of Ω. The following effect occurs: for small enough T the system is approximately controllable in ΩT whereas for larger T < T* a lack of controllability is possible. The subspace of unreachable states is of finite dimension determined by topological characteristics of ΩT.
Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain
Boundary controllability of a chain of serially connected Euler-Bernoulli beams with interior masses.
Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations
We deal with boundary layers and quasi-neutral limits in the drift-diffusion equations. We first show that this limit is unique and determined by a system of two decoupled equations with given initial and boundary conditions. Then we establish the boundary layer equations and prove the existence and uniqueness of solutions with exponential decay. This yields a globally strong convergence (with respect to the domain) of the sequence of solutions and an optimal convergence rate to the quasi-neutral...
Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations
We deal with boundary layers and quasi-neutral limits in the drift-diffusion equations. We first show that this limit is unique and determined by a system of two decoupled equations with given initial and boundary conditions. Then we establish the boundary layer equations and prove the existence and uniqueness of solutions with exponential decay. This yields a globally strong convergence (with respect to the domain) of the sequence of solutions and an optimal convergence rate to the quasi-neutral...
Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem
We study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be εα–periodic, ε being the magnitude of the mean thickness of the layer, and α a positive parameter describing the degree of roughness. For ε tending to zero, we determine the appropriate boundary layer correctors which lead to approximate transmission conditions equivalent to...
Boundary mathematical problems in viscous liquid three-dimensional flows.
Boundary partial regularity for the Navier-Stokes equations.
Boundary regularity of flows under perfect slip boundary conditions
We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.
Boundary stabilization of a coupled system of nondissipative Schrödinger equations.
Boundary stabilization of Maxwell’s equations with space-time variable coefficients
We consider the stabilization of Maxwell’s equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard” identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks.
Boundary stabilization of Maxwell's equations with space-time variable coefficients
We consider the stabilization of Maxwell's equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard" identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks. ...
Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods.