Controllability Problems for the Heat Equation with Variable Coefficients on a Half-Axis Controlled by the Neumann Boundary Condition

2022/11/07 by Fardigola, Larissa, Khalina, Kateryna · 1 citation
#35B30 #35K05 #93B05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2211.03482

Abstract

In the paper, the problems of controllability and approximate controllability are studied for the control system w_t=\frac1ρ(kw_x)_x+γw, .(√\frackρw_x)|_x=0=u, x>0, t∈(0,T), where u is a control, u∈ L^∞(0,T). It is proved that each initial state of the control system is approximately controllable to any target state in a given time T>0. To obtain this result, the transformation operator generated by the equation data ρ, k, γ is applied. The results are illustrated by examples.

Cited by

• Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control

Related

• Reachability and Controllability Problems for the Heat Equation on a\n Half-Axis
• Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Neumann Boundary Condition with a Point-Wise Control
• Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control
• A different look at controllability
• Controllability of impulse controlled systems of heat equations coupled by constant matrices