Approximate controllability for the wave equation

1992 ◽  
pp. 118-124 ◽  
Author(s):  
Doina Cioranescu ◽  
Patrizia Donato ◽  
Enrique Zuazua
Keyword(s):  
Wave Equation ◽  
Approximate Controllability

scholarly journals Approximate Controllability of a 3D Nonlinear Stochastic Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Peng Gao
Keyword(s):  
Wave Equation ◽  
Galerkin Method ◽  
Approximate Controllability ◽  
Well Posedness ◽  
Maxwell System ◽  
Stochastic Wave Equation ◽  
Hilbert Uniqueness Method ◽  
Uniqueness Method ◽  
The Galerkin Method

We study the well-posedness of a 3D nonlinear stochastic wave equation which derives from the Maxwell system by the Galerkin method. Then we study the approximate controllability of this system by the Hilbert uniqueness method.

scholarly journals Localization of energy and localized controllability

2021 ◽  
Author(s):  
Jean-Pierre Puel ◽  
Felipe Chaves-Silva ◽  
Mauricio C. Santos
Keyword(s):  
Wave Equation ◽  
Approximate Controllability ◽  
The Other ◽  
Local Energy ◽  
Open Set ◽  
Other Hand

We will consider both the controlled Schr\"odinger equation and the controlled wave equation on a bounded open set $\Omega$ of $\RR^{N}$ during an interval of time $(0,T)$, with $T>0$. The control is distributed and acts on a nonempty open subdomain $\omega$ of $\Omega$. On the other hand, we consider another open subdomain $D$ of $\Omega$ and the localized energy of the solution in $D$. The first question we want to study is the possibility of obtaining a prescribed value of this local energy at time $T$ by choosing the control adequately.  It turns out that this question is equivalent to a problem of exact or approximate controllability in $D$, which we call localized controllability and which is the second question studied in this article. We obtain sharp results on these two questions and, of course, the answers will require conditions on $\omega$ and $T$ which will be given precisely later on.

Approximate controllability of semilinear impulsive strongly damped wave equation

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Hanzel Larez ◽  
Hugo Leiva ◽  
Jorge Rebaza ◽  
Addison Ríos
Keyword(s):  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Approximate Controllability ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

AbstractRothe's fixed-point theorem is applied to prove the interior approximate controllability of a semilinear impulsive strongly damped wave equation with Dirichlet boundary conditions in the space

scholarly journals Robustness of the controllability for the strongly damped wave equation under the influence of impulses, delays and nonlocal conditions

2019 ◽  
Vol 44 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Hugo Leiva
Keyword(s):  
Wave Equation ◽  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Time Interval ◽  
Short Time Interval ◽  
Damped Wave Equation ◽  
Qualitative Properties ◽  
Strongly Damped Wave Equation ◽  
Fixed Curve ◽  
Strongly Damped

This work proves the following conjecture: impulses, delays, and nonlocal conditions, under some assumptions, do not destroy some posed system qualitative properties since they are themselves intrinsic to it. we verified that the property of controllability is robust under this type of disturbances for the strongly damped wave equation. Specifically, we prove that the interior approximate controllability of linear strongly damped wave equation is not destroyed if we add impulses, nonlocal conditions and a nonlinear perturbation with delay in state. This is done by using new techniques avoiding fixed point theorems employed by A.E. Bashirov et al. In this case the delay help us to prove the approximate controllability of this system by pulling back the control solution to a fixed curve in a short time interval, and from this position, we are able to reach a neighborhood of the final state in time t by using that the corresponding linear strongly damped wave equation is approximately controllable on any interval {t0,T}, 0 < t0 < T.

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