Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2000 / Article

Open Access

Volume 6 |Article ID 649242 | https://doi.org/10.1155/S1024123X00001320

Andras Balogh, Miroslav Krstić, "Burgers' equation with nonlinear boundary feedback: H1 stability, well-posedness and simulation", Mathematical Problems in Engineering, vol. 6, Article ID 649242, 12 pages, 2000. https://doi.org/10.1155/S1024123X00001320

Burgers' equation with nonlinear boundary feedback: H1 stability, well-posedness and simulation

Received17 Jun 1999

Abstract

We consider the viscous Burgers' equation under recently proposed nonlinear boundary conditions and show that it guarantees global asymptotic stabilization and semiglobal exponential stabilization in H1 sense. Our result is global in time and allows arbitrary size of initial data. It strengthens recent results by Byrnes, Gilliam, and Shubov, Ly, Mease, and Titi, and Ito and Yan. The global existence and uniqueness of classical solutions follows from the general theory of quasi-linear parabolic equations. We include a numerical result which illustrates the performance of the boundary controller.

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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