2 Pointwise moving control for the 1-D wave equation

Bottois, Arthur

doi:10.1515/9783110695984-002

Optimization and Control for Partial Differential Equations 2022

DOI: 10.1515/9783110695984-002

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2 Pointwise moving control for the 1-D wave equation

Arthur Bottois¹

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Optimization of non-cylindrical domains for the exact null controllability of the 1D wave equation

2021

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This work is concerned with the null controllability of the one-dimensional wave equation over non-cylindrical distributed domains. The controllability in that case has been obtained by Castro, C\^indea and M\"unch in SIAM J. Control Optim., 52 (2014) for domains satisfying the usual geometric optic condition. We analyze the problem of optimizing the non-cylindrical support $q$ of the control of minimal $L^2(q)$-norm. In this respect, we prove a uniform observability inequality for a class of domains $q$ satisfying the geometric optic condition. The proof based on the d'Alembert formula relies on arguments from graph theory. Numerical experiments are discussed and highlight the influence of the initial condition on the optimal domains.

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Optimization of non-cylindrical domains for the exact null controllability of the 1D wave equation

2021

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2 Pointwise moving control for the 1-D wave equation

Cited by 1 publication

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Optimization of non-cylindrical domains for the exact null controllability of the 1D wave equation

Optimization of non-cylindrical domains for the exact null controllability of the 1D wave equation

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