Stability and decay rate estimates for a nonlinear dispersed flow reactor model with boundary control

TL;DR

This paper analyzes a nonlinear PDE model of a chemical reactor with boundary control, establishing solution existence, stability, and decay rates using semigroup theory and Lyapunov methods.

Contribution

It provides the first rigorous analysis of stability and decay rates for a nonlinear dispersed flow reactor model with boundary feedback control.

Findings

Existence and uniqueness of solutions proved.

Stability of the equilibrium established.

Exponential decay rate of solutions quantified.

Abstract

We investigate a nonlinear parabolic partial differential equation whose boundary conditions contain a single control input. This model describes a chemical reaction of the type ``$A \to $ product'', occurring in a dispersed flow tubular reactor. The existence and uniqueness of solutions to the nonlinear Cauchy problem under consideration are established by applying the theory of strongly continuous semigroups of operators. We also prove the stability of the equilibrium of the closed-loop system with a proposed feedback law. Additionally, using Lyapunov's direct method, we evaluate the exponential decay rate of the solutions.