Hierarchical control for the semilinear parabolic equations with interior degeneracy
Optimization and Control
2023-10-31 v1
Abstract
This paper concerns with the hierarchical control of the semilinear parabolic equations with interior degeneracy. By a Stackelberg-Nash strategy, we consider the linear and semilinear system with one leader and two followers. First, for any given leader, we analyze a Nash equilibrium corresponding to a bi-objective optimal control problem. The existence and uniqueness of the Nash equilibrium is proved, and its characterization is given. Then, we find a leader satisfying the null controllability problem. The key is to establish a new Carleman estimate for a coupled degenerate parabolic system with interior degeneracy.
Keywords
Cite
@article{arxiv.2310.19254,
title = {Hierarchical control for the semilinear parabolic equations with interior degeneracy},
author = {Hang Gao and Wei Yang and Muming Zhang},
journal= {arXiv preprint arXiv:2310.19254},
year = {2023}
}