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Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.

Bao-Zhu Guo, K. Y. Chan (2001)

Revista Matemática Complutense

Using an abstract result on Riesz basis generation for discrete operators in general Hilbert spaces, we show, in this article, that the generalized eigenfunctions of an Euler-Bernoulli beam equation with joint linear feedback control form a Riesz basis for the state space. The spectrum-determined growth condition is hence obtained. Meanwhile, the exponential stability as well as the asymptotic expansion of eigenvalues are also readily obtained by a straightforward computation.

Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators

Giancarlo Mauceri (1981)

Annales de l'institut Fourier

We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in L p norm, at Lebesgue points and almost everywhere. We also prove localization results.

Right inverses for partial differential operators on Fourier hyperfunctions

Michael Langenbruch (2007)

Studia Mathematica

We characterize the partial differential operators P(D) admitting a continuous linear right inverse in the space of Fourier hyperfunctions by means of a dual (Ω̅)-type estimate valid for the bounded holomorphic functions on the characteristic variety V P near ℝ d . The estimate can be transferred to plurisubharmonic functions and is equivalent to a uniform (local) Phragmén-Lindelöf-type condition.

Rigidity for the hyperbolic Monge-Ampère equation

Chun-Chi Lin (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Some properties of nonlinear partial differential equations are naturally associated with the geometry of sets in the space of matrices. In this paper we consider the model case when the compact set  K is contained in the hyperboloid ℋ - 1 , where ℋ - 1 ⊂ 𝕄 sym 2 × 2 , the set of symmetric 2 × 2 matrices. The hyperboloid ℋ - 1 is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampère equation det ∇ 2 u = - 1 . For some compact subsets K ⊂ ℋ - 1 containing a rank-one connection, we show the rigidity property of K by imposing...

Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems

Walid Ben Youssef, Thierry Colin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.

Rigorous results and conjectures on stationary space-periodic 2D turbulence

Sergei B. Kuksin (2006/2007)

Séminaire Équations aux dérivées partielles

We discuss recent results on the inviscid limits for the randomly forced 2D Navier-Stokes equation under periodic boundary conditions, their relevance for the theory of stationary space periodic 2D turbulence and some related conjectures.

Currently displaying 561 – 580 of 614