Small-time Global Controllability of Fourth-Order Parabolic Equations
Published:Dec 29, 2025 09:50
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
- •Investigates the controllability of a fourth-order nonlinear parabolic equation.
- •Demonstrates small-time global approximate controllability with three controls.
- •Establishes small-time global exact controllability to non-zero constant states.
- •Employs geometric control approach and fixed-point arguments.
Reference
“The paper establishes the small-time global approximate controllability of the system using three scalar controls, and then studies the small-time global exact controllability to non-zero constant states.”