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On the controllability of a Boussinesq system for two-way propagation of dispersive waves

On the controllability of a Boussinesq system for two-way propagation of dispersive waves J. Evol. Equ. Journal of Evolution © 2019 Springer Nature Switzerland AG Equations https://doi.org/10.1007/s00028-019-00541-5 On the controllability of a Boussinesq system for two-way propagation of dispersive waves George J. Bautista and Ademir F. Pazoto Abstract. In this paper, we are concerned with a Boussinesq system of Benjamin–Bona–Mahony type equation, posed on a bounded interval, modeling the two-way propagation of surface waves in a uniform horizontal channel filled with an irrotational, incompressible and inviscid liquid under the influence of gravitation. The main focus is on the boundary controllability property, which corresponds to the question of whether the solutions can be driven to a given state at a given final time by means of controls acting at one endpoint of the interval. We first show that the system is not spectrally controllable. This means that no finite linear combination of eigenfunctions associated with the state equations, other than zero, can be steered to zero. Although the system is not spectrally controllable, it can be shown that it is approximately controllable, i.e., any state can be steered arbitrarily close to another state. 1. Introduction It is common knowledge that dispersive wave equations arise as models of various physical phenomena. Because of the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

On the controllability of a Boussinesq system for two-way propagation of dispersive waves

Bautista, George; Pazoto, Ademir
Journal of Evolution Equations , Volume OnlineFirst – Oct 4, 2019
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References (26)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-019-00541-5
Publisher site
See Article on Publisher Site

Abstract

J. Evol. Equ. Journal of Evolution © 2019 Springer Nature Switzerland AG Equations https://doi.org/10.1007/s00028-019-00541-5 On the controllability of a Boussinesq system for two-way propagation of dispersive waves George J. Bautista and Ademir F. Pazoto Abstract. In this paper, we are concerned with a Boussinesq system of Benjamin–Bona–Mahony type equation, posed on a bounded interval, modeling the two-way propagation of surface waves in a uniform horizontal channel filled with an irrotational, incompressible and inviscid liquid under the influence of gravitation. The main focus is on the boundary controllability property, which corresponds to the question of whether the solutions can be driven to a given state at a given final time by means of controls acting at one endpoint of the interval. We first show that the system is not spectrally controllable. This means that no finite linear combination of eigenfunctions associated with the state equations, other than zero, can be steered to zero. Although the system is not spectrally controllable, it can be shown that it is approximately controllable, i.e., any state can be steered arbitrarily close to another state. 1. Introduction It is common knowledge that dispersive wave equations arise as models of various physical phenomena. Because of the

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Journal of Evolution Equations – Springer Journals

Published: Oct 4, 2019

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