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On the double critical-state model for type-II superconductivity in 3D

Yohei Kashima (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current...

On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback

Bao-Zhu Guo, Jun-Min Wang, Cui-Lian Zhou (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability...

On the eigenvalues of a class of hypo-elliptic operators. IV

Johannes Sjöstrand (1980)

Annales de l'institut Fourier

Let P be a selfadjoint classical pseudo-differential operator of order > 1 with non-negative principal symbol on a compact manifold. We assume that P is hypoelliptic with loss of one derivative and semibounded from below. Then exp ( - t P ) , t 0 , is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of P is computed. This paper is a continuation of a series of joint works with A. Menikoff.

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