Hierarchical control for the semilinear parabolic equations with interior degeneracy
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS(2024)
摘要
This paper concerns with the hierarchical control of the semilinear parabolic equations with interior degeneracy. By a Stackelb erg-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. (c) 2024 Elsevier Inc. All rights reserved.
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关键词
Parabolic equation,Interior degeneracy,Stackelb erg -Nash strategy,Carleman estimate
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