Small-time Global Controllability of Fourth-Order Parabolic Equations

This paper explores the controllability of a specific type of fourth-order nonlinear parabolic equation. The research focuses on how to control the system's behavior using time-dependent controls acting through spatial profiles. The key findings are the establishment of small-time global approximate controllability using three controls and small-time global exact controllability to non-zero constant states. This work contributes to the understanding of control theory in higher-order partial differential equations.