Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods

By Enrique Zuazua. SIAM Review, 2005

380 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/bf8a0c46243a9a5da927a0551f1575dc74443099

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In Computational Mechanics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

The Wave Equation: Control and Numerics (2012, methodology): “This paper is essentially an updated version of [114], in which we collect most of the more recent developments.”
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems (2011, background): “This can be viewed, for instance, through the Kalman rank condition for the control of finite-dimensional systems (see [7,38]), which we shall discuss in detail in Section 2.”
A SYSTEMATIC METHOD FOR BUILDING SMOOTH CONTROLS FOR SMOOTH DATA (2010, background): “In particular, one can design from it and the results on the observability of space semi-discrete wave equations (see [10], [24], [6], .”
Uniformly exponentially stable approximations for a class of second order evolution equations (2007, methodology): “We refer to the review paper Zuazua [ 20 ] for more details and extensive references.”
Inverse problems: A Bayesian perspective (2010, background): “…difference spatial discretization of the first-order wave equation gives rise to a linear system of ordinary differential equations which is controllable, in any finite time, to a given final state; asking the controllability question before discretization is key to understanding (Zuazua 2005).”
Uniformly exponentially stable approximations for a class of damped systems (2009, background): “We refer to the review article [32] for more references.”
On the observability of time-discrete conservative linear systems (2008, methodology): “Note that this type of observability inequalities appears naturally when dealing with stabilization and controllability problems (see, for instance, [15], [25] and [ 29 ]).”