Boundary Control of Korteweg-de Vries and Kuramoto-Sivashinsky PDEs
The Korteweg-de Vries (KdV) and the Kuramoto-Sivashinsky (KS) partial differential equations are used to model nonlinear propagation of one-dimensional phenomena. The KdV equation is used in fluid mechanics to describe wave propagation in shallow water surfaces, while the KS equation models front propagation in reaction-diffusion systems. In this article, the boundary control of these equations is considered when they are posed on a bounded interval. Different choices of controls are studied for each equation.
KeywordsControllability Stabilizability Higher-order partial differential equations Dispersive equations Parabolic equations
- Takahashi T (2017) Boundary local null-controllability of the Kuramoto-Sivashinsky equation. Math Control Signals Syst 29:Art. 2, 1–21Google Scholar