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<p>This work continues the results presented in [<CitationRef CitationID="CR1">1</CitationRef>] where a hierarchical control problem is solved. Our first goal is the case of both controls acting on the boundary. The follower control solves a null controllability problem, and the leader minimizes a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> cost functional. Additionally, we solve the case where one control acts on the boundary and the other on an open subset of the domain. More precisely, we prove the existence and uniqueness of a leader-follower couple and give some techniques to solve the problem.</p>

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A Stackelberg strategy for the semi-linear heat equation with boundary controls

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Jose Antonio Villa

摘要

This work continues the results presented in [1] where a hierarchical control problem is solved. Our first goal is the case of both controls acting on the boundary. The follower control solves a null controllability problem, and the leader minimizes a \(L^2\) L 2 cost functional. Additionally, we solve the case where one control acts on the boundary and the other on an open subset of the domain. More precisely, we prove the existence and uniqueness of a leader-follower couple and give some techniques to solve the problem.