Stabilization of the Korteweg-De Vries equation with localized damping

By G. Perla Menzala, Carlos F. Vasconcellos, Enrique Zuazua. 2002

176 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/47a0433c9babfb6d41151cc343c198813e388f05

How researchers see this paper

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In Control and Systems Engineering

1. Jean-Michel Coron
2. Qi Lu
3. Ademir Fernando Pazoto
4. Bingyu Zhang
5. Lionel Rosier
6. Felipe Linares
7. R. A. Capistrano–Filho
8. G. Doronin

In Mathematical Physics

1. Jean-Michel Coron
2. Bingyu Zhang
3. Ademir Fernando Pazoto
4. Lionel Rosier
5. Qi Lu
6. Felipe Linares
7. R. A. Capistrano–Filho
8. Fágner D. Araruna

In Statistical and Nonlinear Physics

1. Lionel Rosier
2. Bingyu Zhang
3. Ademir Fernando Pazoto
4. Qi Lu
5. R. A. Capistrano–Filho
6. Fágner D. Araruna
7. Jaime H. Ortega
8. Sorin Daniel Micu

Citations in the corpus

• Unique continuation and decay for the Korteweg-de Vries equation with localized damping (2005, methodology): “Statement of the main results For the sake of completeness, we state the existence and uniqueness result for problem (1) obtained in [12]: Theorem 2.”
• Energy decay for the modified Kawahara equation posed in a bounded domain (2012, methodology): “To overcome these difficulties, a damping of the type a(x)u was introduced in [22] to stabilize the KdV system.”
• Control of a Korteweg-de Vries equation: A tutorial (2013, unknown): “[35, 33] Let L > 0, a = a(x) satisfying (6), and R > 0.”
• Local rapid stabilization for a Korteweg–de Vries equation with a Neumann boundary control on the right (2013, background): “For KdV equations with internal feedback controls, we refer to [14, 18, 19, 20, 23, 24, 25, 26] and the rich references therein, as well as the self-contained survey paper [3].”
• CONTROL AND STABILIZATION OF A FAMILY OF BOUSSINESQ SYSTEMS (2009, background): “In order to stabilize large amplitude solutions and to remove the length restriction on L, Perla Menzala, Vasconcellos, and Zuazua [28] introduced an extra localized feedback control to (1.”
• On the exponential decay of the critical generalized Korteweg-de Vries equation with localized damping (2007, background): “Later on, performing as in [9], the general case was solved in [11] showing that solutions vanishing on any subinterval are necessarily smooth, which yields enough regularity on u to apply the unique continuation results obtained in [15].”