## Abstract

We consider the problem of local exponential stabilization of the nonlinear Boussinesq equations with control acting on portion of the boundary. In particular, given a steady state solution on an bounded and connected domain ^{R2}, we show that a finite number of controls acting on a part of the boundary through Neumann/Robin boundary conditions is sufficient to stabilize the full nonlinear equations in a neighborhood of this steady state solution. Dirichlet boundary conditions are imposed on the rest of the boundary. We prove that a stabilizing feedback control law can be obtained by solving a Linear Quadratic Regulator (LQR) problem for the linearized Boussinesq equations. Numerical result are provided for a 2D problem to illustrate the ideas.

Original language | English (US) |
---|---|

Pages (from-to) | 2170-2191 |

Number of pages | 22 |

Journal | Computers and Mathematics with Applications |

Volume | 71 |

Issue number | 11 |

DOIs | |

State | Published - Jun 1 2016 |

### Bibliographical note

Funding Information:This research was supported in part by the DOE contract DE-EE0004261 under subcontract # 4345-VT-DOE-4261 from Penn State University .

## Keywords

- Feedback control
- Partial differential equations
- Thermal fluid systems