SIAM Journal on Control and Optimization· 2026Q1
Rapid Boundary Stabilization of One-Dimensional Nonlinear Parabolic Equations
- 3citations
- Q1SCImago
- 2026year
Short summary
A novel boundary feedback control method achieves rapid exponential stabilization for one-dimensional nonlinear parabolic equations, combining existing frameworks with a frequency Lyapunov method.
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Key points
- Introduced a boundary feedback control for rapid exponential stabilization of 1D nonlinear parabolic equations.
- Combined Coron and Trélat's framework with the frequency Lyapunov method.
- Achieved local rapid exponential stabilization under minimal low-frequency structural requirements.
- Demonstrated global stabilization for dissipative superlinear heat and viscous Burgers equations.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract. We investigate the rapid boundary exponential stabilization of one-dimensional nonlinear parabolic equations by combining the framework of Coron and Trélat [ SIAM J. Control Optim., 43 (2004), pp. 549–569] with the frequency Lyapunov method introduced by Xiang [ ESAIM Control Optim. Calc. Var., 30 (2024), 40]. We construct a boundary feedback control that achieves the local rapid exponential stabilization under minimal low-frequency structural requirements. This design, when coupled with the intrinsic global dissipative dynamics of the equations, yields global stabilization results for both dissipative superlinear heat equations and viscous Burgers equations.
The authors' abstract, as published at the source. SIAM Journal on Control and Optimization, 2026 · DOI ↗
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Field: Control and Systems Engineering
Control and Systems EngineeringEngineering