Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
MC 5158
Rasha Jamal, Applied Mathematics, University of Waterloo
A Single Bounded Input Control to the Kuramoto-Sivashinsky Equation
The Kuramoto-Sivashinsky (KS) equation is a nonlinear partial differential equation that is first-order in time and fourth-order in space. It models reaction-diffusion systems and is related to various pattern formation phenomena where turbulence or chaos appear. For instance, it models long wave motions of the liquid film over a vertical plane. For certain parameter values of interest, this equation is unstable. This is shown by analyzing the stability of the linearized system and showing that the nonlinear C0-semigroup corresponding to the nonlinear system is Frechet differentiable. There are a number of papers establishing the stabilization of this equation via boundary control. In this talk, we consider distributed control with a single control variable for the KS equation with periodic boundary conditions. First, we show that stabilizing the linearized KS equation implies local exponential stability of the KS equation. This is done by establishing Frechet differentiability of the associated semigroup and showing that it is equal to the semigroup generated by the linearization of the equation. Next, we construct a single input-feedback control that locally exponentially stabilizes the KS equation. Finally, we control the KS equation from one equilibrium solution to another.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
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