Null controllability for wave equations with memory

Lu Q, Zhang X, Zuazua E (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Journal De Mathematiques Pures Et Appliquees Elsevier

Book Volume: 108

Pages Range: 500-531

Journal Issue: 4

DOI: 10.1016/j.matpur.2017.05.001

Abstract

We study the memory-type null controllability property for wave equations involving memory terms. The goal is not only to drive the displacement and the velocity (of the considered wave) to rest at some time-instant but also to require the memory term to vanish at the same time, ensuring that the whole process reaches the equilibrium. This memory-type null controllability problem can be reduced to the classical null controllability property for a coupled PDE–ODE system. The latter can be viewed as a degenerate system of wave equations, in which the velocity of propagation for the ODE component vanishes. This fact requires the support of the control to move to ensure the memory-type null controllability to hold, under the so-called Moving Geometric Control Condition. The control result is proved by duality by means of an observability inequality which employs measurements done on a moving observation open subset of the domain where the waves propagate.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Sichuan University (SCU) / 四川大学 CN China (CN) University of Deusto / Universidad de Deusto ES Spain (ES)

How to cite

APA:

Lu, Q., Zhang, X., & Zuazua, E. (2017). Null controllability for wave equations with memory. Journal De Mathematiques Pures Et Appliquees, 108(4), 500-531. https://dx.doi.org/10.1016/j.matpur.2017.05.001

MLA:

Lu, Qi, Xu Zhang, and Enrique Zuazua. "Null controllability for wave equations with memory." Journal De Mathematiques Pures Et Appliquees 108.4 (2017): 500-531.

BibTeX: Download