A concept of phase asymptotic semiflow is defined. It is shown that any Lagrange stable orbit at which the semiflow is phase asymptotic limits to a stable periodic orbit. A Lagrange stable solution of a C 1 differential equation is considered. When the second compound of the variational equation with respect to this solution is uniformly asymptotically stable and the omega limit set contains no...

One of recent achievements in the field of nonlinear H∞ optimal control theories for Euler-Lagrange systems is the analytic solution to the Hamilton-JacobiIsaccs (HJI) equation associated to the so-called nonlinear H∞ inverse-optimal control [1]. In this paper, we address the problem of nonlinear H∞ optimal control design for an Euler-Lagrange system, rather than the inverse-optimal problem. By...

We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagra...

Finite element methods are known to produce spurious oscillations when the transport equation is solved. In this paper, a variational formulation for the transport equation is proposed, and by introducing a positivity constraint combined with a penalization of the total variation of the solution, a discrete maximum principle is verified for lagrange first order finite element methods. Moreover,...

Prescribing, by conformal transformation, the k-elementary symmetric polynomial of the Schouten tensor σk(P) to be constant is a generalisation of the Yamabe problem. On compact Riemannian n-manifolds we show that, for 3 ≤ k ≤ n, this prescription equation is an Euler-Lagrange equation of some action if and only if the structure is locally conformally flat.

Physical based and geometric based variational techniques for surface construction have been shown to be advanced methods for designing high quality surfaces in the fields of CAD and CAGD. In this paper, we derive a Euler-Lagrange equation from a geometric invariant curvature integral functional–the integral about the mean curvature gradient. Using this Euler-Lagrange equation, we construct a s...