All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 35 Next

Displaying 681 – 700 of 3659

Showing per page

Controller design for bush-type 1-d wave networks∗

Yaxuan Zhang, Genqi Xu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...

Controller design for bush-type 1-d wave networks

Yaxuan Zhang, Genqi Xu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...

Controller design for bush-type 1-d wave networks∗

Yaxuan Zhang, Genqi Xu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...

Convergence of a fully discrete finite element method for a degenerate parabolic system modelling nematic liquid crystals with variable degree of orientation

John W. Barrett, Xiaobing Feng, Andreas Prohl (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a degenerate parabolic system which models the evolution of nematic liquid crystal with variable degree of orientation. The system is a slight modification to that proposed in [Calderer et al., SIAM J. Math. Anal.33 (2002) 1033–1047], which is a special case of Ericksen's general continuum model in [Ericksen, Arch. Ration. Mech. Anal.113 (1991) 97–120]. We prove the global existence of weak solutions by passing to the limit in a regularized system. Moreover, we propose a practical...

Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation

Guillaume Legendre, Takéo Takahashi (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a numerical scheme to compute the motion of a two-dimensional rigid body in a viscous fluid. Our method combines the method of characteristics with a finite element approximation to solve an ALE formulation of the problem. We derive error estimates implying the convergence of the scheme.

Convergence of a method for solving the magnetostatic field in nonlinear media

Jozef Kačur, Jindřich Nečas, Josef Polák, Jiří Souček (1968)

Aplikace matematiky

For solving the boundary-value problem for potential of a stationary magnetic field in two dimensions in ferromagnetics it is possible to use a linearization based on the succesive approximations. In this paper the convergence of this method is proved under some conditions.

Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics

Francesca Da Lio, N. Forcadel, Régis Monneau (2008)

Journal of the European Mathematical Society

We prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. The equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, which arises in the theory of dislocation dynamics. We show that if an anisotropic mean curvature motion is approximated by equations of this type then it is always of variational type, whereas the converse is true only in dimension two.

Convergence of a variational lagrangian scheme for a nonlinear drift diffusion equation

Daniel Matthes, Horst Osberger (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation’s gradient flow structure with respect to the Wasserstein distance. The scheme inherits various properties from the continuous flow, like entropy monotonicity, mass preservation, metric contraction and minimum/ maximum principles. As the main result, we give a proof of convergence in the limit of vanishing mesh size under a CFL-type condition. We...

Convergence of gradient-based algorithms for the Hartree-Fock equations

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) 170]. In this paper, we prove the convergence of...

Convergence of gradient-based algorithms for the Hartree-Fock equations

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) 170]. In this paper, we prove the convergence of...

Convergence of gradient-based algorithms for the Hartree-Fock equations∗

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) ...

Convergence of minimax structures and continuation of critical points for singularly perturbed systems

Benedetta Noris, Hugo Tavares, Susanna Terracini, Gianmaria Verzini (2012)

Journal of the European Mathematical Society

In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system - Δ u + u 3 + β u v 2 = λ u , - Δ v + v 3 + β u 2 v = μ v , u , v ∈ H 0 1 ( Ω ) , u , v > 0 , as the interspecies scattering length β goes to + ∞ . For this system we consider the associated energy functionals J β , β ∈ ( 0 , + ∞ ) , with L 2 -mass constraints, which limit J ∞ (as β → + ∞ ) is strongly irregular. For such functionals, we construct multiple critical points via a common...

Convergence of the rotating fluids system in a domain with rough boundaries

David Gérard-Varet (2003)

Journées équations aux dérivées partielles

We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size ϵ . We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as ϵ goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with the classical...

Currently displaying 681 – 700 of 3659