Observability Inequality from Measurable Sets for Degenerate Parabolic Equations and its Applications

Yuanhang Liu (), Weijia Wu (), Donghui Yang () and Can Zhang ()
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Yuanhang Liu: Central South University
Weijia Wu: Central South University
Donghui Yang: Central South University
Can Zhang: Wuhan University

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 3, No 5, 1017-1055

Abstract: Abstract In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, along with the telescoping series method, to establish an observability inequality for the degenerate parabolic equation over measurable subsets in the time-space domain. As a direct application, we formulate a captivating Stackelberg–Nash game problem and provide a proof of the existence of its equilibrium. Additionally, we characterize the set of Stackelberg–Nash equilibria and delve into the analysis of a norm optimal control problem.

Keywords: Observability inequality; Measurable sets; Stackelberg–Nash equilibrium; Degenerate parabolic equations; 93B05; 93B07 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02359-1

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