GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS

By Jean-Michel Coron, Emmanuel Trélat. 2006

93 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/52b5987f9d2305bedeadac1fa4b9bdc84cc33dc7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Emmanuel Trélat
2. Enrique Zuazua
3. Eduardo Cerpa
4. Christophe Prieur
5. Frédéric Mazenc
6. Emmanuelle Crépeau
7. Benedetto Piccoli
8. Massimo Fornasier

In Control and Systems Engineering

1. Eduardo Cerpa
2. Emmanuel Trélat
3. Enrique Zuazua
4. Christophe Prieur
5. Frédéric Mazenc
6. Emmanuelle Crépeau
7. Benedetto Piccoli
8. Sylvain Ervedoza

In Mathematical Physics

1. Eduardo Cerpa
2. Enrique Zuazua
3. Emmanuel Trélat
4. Christophe Prieur
5. Frédéric Mazenc
6. Emmanuelle Crépeau
7. Massimo Fornasier
8. Sylvain Ervedoza

Citations in the corpus

• Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain (2009, methodology): “This method and others such as quasi-static deformations (see [1,12,13] and [10, Chapter 7]) and the return method (see [1,6–8] and [10, Chapter 6]) are very useful to deal with nonlinear systems and to get properties which are not a consequence of the linearized system behavior.”
• Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation (2009, unknown): “(13) Proof.”
• Sparse stabilization and optimal control of the Cucker-Smale model (2013, background): “This is a partial but global controllability result, whose proof follows the strategy developed in [15, 16] for controlling heat and wave equations on steady-states.”
• The turnpike property in finite-dimensional nonlinear optimal control (2014, methodology): “ontrol problems by steady-state formulations has also been used in order to derive controllability results for dicult unstable PDE control problems (see [18] for semilinear explosive heat equations, [19] for semilinear explosive wave equations, [44] for Couette ows with Navier-Stokes equations). Thi”
• Strict Lyapunov functions for semilinear parabolic partial differential equations (2011, methodology): “a Lyapunov function whose derivative along the trajectories of the system which is considered is non-positive (but not necessarily negative definite), and in [8] the controllability of the wave equation is demonstrated via a Lyapunov function.”