A note on the necessity of filtering mechanism for polynomial observability of time-discrete wave equation
Journal Title: Карпатські математичні публікації - Year 2017, Vol 9, Issue 1
Abstract
The problem of uniform polynomial observability was recently analyzed. It is shown that, when the continuous model is uniformly polynomially observable, it is sufficient to filter initial data to derive uniform polynomial observability inequalities for suitable time-discretization schemes. In this note, we prove that a filtering mechanism of high frequency modes is necessary to obtain uniform polynomial observability. More precisely, we give a counterexample which proves that this latter fails without filtering the initial data for time semi-discrete approximations of the wave equation.
Authors and Affiliations
Z. Hajjej
Keywords
Related Articles
- EP ID EP325103
- DOI 10.15330/cmp.9.1.98-103
- Views 75
- Downloads 0
Application of the functional calculus to solving of infinite dimensional heat equation
In this paper we study infinite dimensional heat equation associated with the Gross Laplacian. Using the functional calculus method, we obtain the solution of appropriate Cauchy problem in the space of polynomial ultradi...
Extensions of multilinear mappings to powers of linear spaces
We consider the question of the possibility to recover a multilinear mapping from the restriction to the diagonal of its extension to a Cartesian power of a space.
On properties of the solutions of the Weber equation
Growth, convexity and the l-index boundedness of the functions α(z) and β(z), such that α(z4) and zβ(z4) are linear independent solutions of the Weber equation w′′−(z24−ν−12)w=0 if ν=−12 are investigated.
Coincidence point theorems for $\varphi-\psi-$contraction mappings in metric spaces involving a graph
Some new coupled coincidence and coupled common fixed point theorems for $\varphi-\psi-$contraction mappings are established. We have also an application to some integral system to support the results.
Convergence in Lp[0,2π]-metric of logarithmic derivative and angular υ -density for zeros of entire function of slowly growth
The subclass of a zero order entire function f is pointed out for which the existence of angular υ-density for zeros of entire function of zero order is equivalent to convergence in Lp[0,2π] -metric of its logarithmic d...