Reachability and Controllability Problems for the Heat Equation on a\n Half-Axis

2018/12/28 by L. V. Fardigola, Fardigola, Larissa, Kateryna Khalina +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1812.11208

openalex publication_date 2018/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, problems of controllability, approximate controllability,\nreachability and approximate reachability are studied for the control system\nw_t=w_xx, w(0,\⋅)=u, x>0, t\∈(0,T), where u\∈ L^\∞(0,T) is\na control. It is proved that each end state of this system is approximately\nreachable in a given time T, and each its initial state is approximately\ncontrollable in a given time T. A necessary and sufficient condition for\nreachability in a given time T is obtained in terms of solvability a Markov\npower moment problem. It is also shown that there is no initial state that is\nnull-controllable in a given time T. The results are illustrated by examples.\n

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