English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This article considers the linear 1-d Schrodinger equation in (0 ,π ) perturbed by a vanishing viscosity term depending on a small parameter e> 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls ve as e goes to zero. It is shown that, for any time T sufficiently large but independent of e and for each initial datum in H 1 (0 ,π ), there exists a uniformly bounded family of controls (ve)e in L 2 (0 ,T ) acting on the extremity x = π. Any weak limit of this family is a control for the Schrodinger equation.

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity