Conservation laws for the nonlinear Schrödinger equation
Consistency, accuracy and entropy behaviour of remeshed particle methods
In this paper we analyze the consistency, the accuracy and some entropy properties of particle methods with remeshing in the case of a scalar one-dimensional conservation law. As in [G.-H. Cottet and L. Weynans, C. R. Acad. Sci. Paris, Ser. I 343 (2006) 51–56] we re-write particle methods with remeshing in the finite-difference formalism. This allows us to prove the consistency of these methods, and accuracy properties related to the accuracy of interpolation kernels. Cottet and Magni devised recently...
Consistency, accuracy and entropy behaviour of remeshed particle methods
In this paper we analyze the consistency, the accuracy and some entropy properties of particle methods with remeshing in the case of a scalar one-dimensional conservation law. As in [G.-H. Cottet and L. Weynans, C. R. Acad. Sci. Paris, Ser. I 343 (2006) 51–56] we re-write particle methods with remeshing in the finite-difference formalism. This allows us to prove the consistency of these methods, and accuracy properties related to the accuracy of...
Consistent algorithms marching along characteristics for the numerical solution of the Boltzmann equation.
Consistent streamline residual-based artificial viscosity stabilization for numerical simulation of incompressible turbulent flow by isogeometric analysis
In this paper, we propose a new stabilization technique for numerical simulation of incompressible turbulent flow by solving Reynolds-averaged Navier-Stokes equations closed by the SST - turbulence model. The stabilization scheme is constructed such that it is consistent in the sense used in the finite element method, artificial diffusion is added only in the direction of convection and it is based on a purely nonlinear approach. We present numerical results obtained by our in-house incompressible...
Constructing soliton and kink solutions of PDE models in transport and biology.
Construction BKW pour l'opérateur de Dirac. Cas d'un potentiel périodique
Construction de solutions pour les équations de Korteweg-de Vries généralisées
Construction of Approximative and Almost Periodic Solutions of Perturbed Linear Schrödinger and Wave Equations.
Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
Continuity of the Darcy's law in the low-volume fraction limit
Continuous dependence and stability for non linear dispersive and dissipative waves
Continuous dependence for the Brinkman equations of flow in double-diffusive convection.
Continuous dependence in for discontinuous solutions of the viscous -system
Continuous dependence of 2D large scale primitive equations on the boundary conditions in oceanic dynamics
In this paper, we consider an initial boundary value problem for the two-dimensional primitive equations of large scale oceanic dynamics. Assuming that the depth of the ocean is a positive constant, we establish rigorous a priori bounds of the solution to problem. With the aid of these a priori bounds, the continuous dependence of the solution on changes in the boundary terms is obtained.
Contributo allo studio dei fenomeni di trasporto della carica minoritaria in regioni quasi neutre di semiconduttori fortemente e disuniformemente drogati. Riduzione del problema ad equazioni integrali
Transport phenomena of minority carriers in quasi neutral regions of heavily doped semiconductors are considered for the case of one-dimensional stationary flow and their study is reduced to a Fredholm integral equation of the second kind, the kernel and the known term of which are built from known functions of the doping arbitrarily distributed in space. The advantage of the method consists, among other things, in having all the coefficients of the differential equations and of the boundary conditions...
Control for Schrödinger operators on 2-tori: rough potentials
For the Schrödinger equation, on a torus, an arbitrary non-empty open set provides control and observability of the solution: . We show that the same result remains true for where , and is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for and conjectured for . The higher dimensional generalization remains open for .
Control for the Sine-Gordon equation
In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
Control for the sine-gordon equation
In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
Control of the continuity equation with a non local flow
This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary ...