2011/09/21 by Grzegorz Dudziuk, Dudziuk, Grzegorz, Marek Niezgódka +1
Computer Science · Materials Science · Mathematics · #35Q79 #35Q93 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Solidification and crystal growth phenomena #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1109.4530
openalex publication_date 2011/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A system of a parabolic partial differential equation coupled with ordinary differential inclusions that arises from a closed-loop control problem for a thermodynamic process governed by the Allen-Cahn diffusion reaction model is studied. A feedback law for the closed-loop control is proposed and implemented in the case of a finite number of control devices located inside the process domain basing on the process dynamics observed at a finite number of measurement points. The existence of solutions to the discussed system of differential equations is proved with the use of a generalization of the Kakutani fixed point theorem.