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Burgers' equation with nonlinear boundary feedback: H 1 stability, well-posedness and simulation

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  • Andras Balogh
  • Miroslav Krstić

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 H 1 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.

Suggested Citation

  • Andras Balogh & Miroslav Krstić, 2000. "Burgers' equation with nonlinear boundary feedback: H 1 stability, well-posedness and simulation," Mathematical Problems in Engineering, Hindawi, vol. 6, pages 1-12, January.
    • Handle: RePEc:hin:jnlmpe:649242
    DOI: 10.1155/S1024123X00001320
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