January & February  2009, 23(1&2): 299-313. doi: 10.3934/dcds.2009.23.299

On global controllability of 2-D Burgers equation

1. 

Department of Mathematics, Colorado State University,101 Weber Building, Fort Colins, CO 80523-1784, United States

2. 

Laboratoire de Mathématiques de Versailles, Université de Versailles - St. Quentin, 45 Avenue des Etats Unis, 78035 Versailles, France

Received  May 2007 Revised  February 2008 Published  September 2008

We study the question of global controllability for the two-dimensional Burgers equation when the control acts on a part $\Gamma_{1}$ of the boundary $\Gamma$. We prove global controllability when $\Gamma_{1}$ is the whole boundary or in a specific geometrical situation when $\Gamma_{0}=\Gamma \setminus \Gamma_{1}$ is contained in a parallel to the first bisector line. We also show with a counterexample that $\Gamma_{1}$ cannot be taken any part of the boundary.
Citation: Oleg Yu. Imanuvilov, Jean Pierre Puel. On global controllability of 2-D Burgers equation. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 299-313. doi: 10.3934/dcds.2009.23.299
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