Exponential Decay for a Boundary-Controlled Nonlinear Parabolic Reactor Model
Yevgeniia Yevgenieva, Alexander Zuyev, Christophe Prieur, Peter Benner
TL;DR
This paper analyzes the exponential stability of a nonlinear parabolic reactor model with boundary feedback control, providing conditions for stability, explicit decay rate estimates, and numerical validation.
Contribution
It introduces new stability conditions and explicit decay rate estimates for a boundary-controlled nonlinear parabolic reactor model.
Findings
Derived sufficient conditions for exponential stability.
Provided explicit decay rate estimates.
Numerical simulations confirm the theoretical results.
Abstract
We study an axial dispersion tubular reactor model governed by a nonlinear parabolic equation with Robin-type boundary conditions and boundary feedback control. We derive sufficient conditions for the exponential stability of the steady-state solution of the closed-loop system and provide an explicit estimate of the decay rate. In addition, numerical simulations are presented to illustrate the sharpness of the obtained decay rate for different choices of the feedback gain parameter.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Mathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Dynamics and Pattern Formation