Spacetime finite element methods for control problems subject to the wave equation
We consider the null controllability problem for the wave equation, and analyse a stabilized
finite element method formulated on a global, unstructured spacetime mesh. We prove error …
finite element method formulated on a global, unstructured spacetime mesh. We prove error …
A mixed formulation for the direct approximation of the control of minimal -norm for linear type wave equations
This paper deals with the numerical computation of null controls for the wave equation with a
potential. The goal is to compute approximations of controls that drive the solution from a …
potential. The goal is to compute approximations of controls that drive the solution from a …
Control of partial differential equations via physics-informed neural networks
CJ García-Cervera, M Kessler, F Periago - Journal of Optimization Theory …, 2023 - Springer
This paper addresses the numerical resolution of controllability problems for partial
differential equations (PDEs) by using physics-informed neural networks. Error estimates for …
differential equations (PDEs) by using physics-informed neural networks. Error estimates for …
An approximation method for exact controls of vibrating systems
We propose a new method for the approximation of exact controls of a second order infinite
dimensional system with bounded input operator. The algorithm combines Russell's …
dimensional system with bounded input operator. The algorithm combines Russell's …
[HTML][HTML] Energy decay for the linear Klein–Gordon equation and boundary control
RSO Nunes, WD Bastos - Journal of Mathematical Analysis and …, 2014 - Elsevier
In this work we study the asymptotic behavior of the solutions of the linear Klein–Gordon
equation in RN, N⩾ 1. We prove that local energy of solutions to the Cauchy problem decays …
equation in RN, N⩾ 1. We prove that local energy of solutions to the Cauchy problem decays …
Numerical control of a semilinear wave equation on an interval
We are concerned with the numerical exact controllability of the semilinear wave equation
on the interval (0, 1). We introduce a Picard iterative scheme yielding a sequence of …
on the interval (0, 1). We introduce a Picard iterative scheme yielding a sequence of …
On exact boundary controllability for linearly coupled wave equations
WD Bastos, A Spezamiglio, CA Raposo - Journal of mathematical analysis …, 2011 - Elsevier
On exact boundary controllability for linearly coupled wave equations Page 1 J. Math. Anal.
Appl. 381 (2011) 557–564 Contents lists available at ScienceDirect Journal of Mathematical …
Appl. 381 (2011) 557–564 Contents lists available at ScienceDirect Journal of Mathematical …
Boundary controllability of a nonlinear elastic body
AN Ardekany, ZM Hosseini - Acta Mechanica, 2024 - Springer
This paper addresses the exact controllability of vibrations in a three-dimensional Cosserat
elastic solid body using mathematical techniques such as operator theory and semigroup …
elastic solid body using mathematical techniques such as operator theory and semigroup …
Waves, damped wave and observation
KD Phung - Some problems on nonlinear hyperbolic equations and …, 2010 - World Scientific
Waves, Damped Wave and Observation* 1 The wave equation and observation Page 1 386
Waves, Damped Wave and Observation* Kim Dang Phung Yangtze Center of Mathematics …
Waves, Damped Wave and Observation* Kim Dang Phung Yangtze Center of Mathematics …
An approximation method for exact controls of vibrating systems with numerical viscosity
We analyze a method for the approximation of exact controls of a second order infinite
dimensional system with bounded input operator. The algorithm combines Russell's …
dimensional system with bounded input operator. The algorithm combines Russell's …