3 papers
math.OC2026
Quantitative linear approximation for controllability of quasi-linear parabolic equations
Manish Kumar, Xu Liu, Xu Zhang
This paper studies the relationship between the controllability of a quasi-linear parabolic equation and that of its linear counterpart. Under suitable assumptions, we prove that f…
math.OC2026
Optimal control problems for quasi-linear parabolic equations and their linear approximations
Xu Liu, Meisai Wang, Xu Zhang
Motivated by thermal diffusion models, a controlled quasi-linear parabolic equation can be formally replaced by its linear approximation, when the initial datum, target and control…
math.OC2024
A Class of Multi-Objective Control Problems for Quasi-linear Parabolic Equations
Yanming Dong, Xu Liu, Xu Zhang
This paper is devoted to studying a multi-objective control problem for a class of multi-dimensional quasi-linear parabolic equations. The considered system is driven by a leader c…