In this paper, we provide a Schwarz preconditioner for the hybridized versions of the Raviart-Thomas and Brezzi-Douglas-Marini mixed methods. The preconditioner is for the linear equation for Lagrange multipliers arrived at by eliminating the flux as well as the primal variable. We also prove a condition number estimate for this equation when no preconditioner is used. Although preconditioners ...

Equation (1.1)ρ is called the mean field equation because it often arises in the context of statistical mechanics of point vortices in the mean field limits. Recently, there has been interest in (1.1)ρ because it also arises from the Chern-Simons-Higgs model vortex theory when some parameter tends to zero. (For these recent developments, we refer the readers to [5], [2], [3], [10], [11], [13], ...

In this paper energy method is used to calculate rotor response with loose rotating disk on it. System equation of motion is obtained based on energy method and Lagrange equation. Mathematical modeling of loose disk in a rotor bearing system has resulted in terms similar to unbalance and gyroscopic effect in the system equation of motion. The effect of loose disk axial position and orthotropic ...

In this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical Lagrange finite elements. Th...

The infinity Laplace equation ∆∞u = 0 arose originally as a sort of Euler–Lagrange equation governing the absolute minimizer for the L∞ variational problem of minimizing the functional ess-supU |Du|. The more general functional ess-supUF (x, u, Du) leads similarly to the so-called Aronsson equation AF [u] = 0. In this paper we show that these PDE operators and various interesting generalization...

This paper constructs the penalty cost functional for optimizing the two-dimensional control operator of the energized wave equation. In some multiplier methods such as the Lagrange multipliers and Pontrygean maximum principle, the cost of merging the constraint equation to the integral quadratic objective functional to obtain an unconstraint equation is normally guessed or obtained from the fi...

In this paper, smooth Chua’s equation is generalized to a higher order system from a special viewpoint of interconnected systems. Simple conditions for Lagrange stability are established. And a detailed Lagrange stable region analysis is given for the canonical Chua’s oscillator. In addition, a new nonlinearly coupled Chua’s circuit that appeared in the recent literature is also discussed and a...

The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua’s periodic table. Newly defined potential functions for general (,) elements are used for the construction of generalized Lagrangians and generalized dissipative functions. Also procedures of drawing the Euler-Lagrange equations are demonstrated.

The dynamics of randomly forced Burgers and Euler-Lagrange equations in S 1 × R d−1 in the case when there is only one one-sided minimizer in a compact subset of S 1 × R d−1 is studied. The existence of random invariant periodic minimizer orbits and periodicity of the stationary solution of the stochastic Burgers equations are obtained.

We construct rigidly supersymmetric bulk-plus-boundary actions, both in x-space and in superspace. For each standard supersymmetric bulk action a minimal supersymmetric bulk-plus-boundary action follows from an extended F or D-term formula. Additional separately supersymmetric boundary actions can be systematically constructed using co-dimension one multiplets (boundary superfields). We also di...