# Global Stabilization of Two Dimensional Viscous Burgers' Equation by Nonlinear Neumann Boundary Feedback Control and its Finite Element Analysis

arXiv: https://arxiv.org/abs/1812.02083 · HTML: https://mlsanity.com/paper/1812.02083/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2018.

## Built on by (most cited first, 2 of 2)

- [RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations](https://mlsanity.com/paper/2509.01234/) (2025)
- [Convolutional Autoencoders, Clustering and POD for Low-dimensional Parametrization of Navier-Stokes Equations](https://mlsanity.com/paper/2302.01278/) (2023)

## Abstract (arXiv)

In this article, global stabilization results for the two dimensional (2D) viscous Burgers' equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear Neumann boundary feedback control law. Then, applying C0-conforming finite element method in spatial direction, optimal error estimates in L^∞(L2) and in L^∞(H1)- norms for the state variable and convergence result for the boundary feedback control law are derived. All the results preserve exponential stabilization property. Finally, several numerical experiments are conducted to confirm our theoretical findings.