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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2019

A topological obstruction to the controllability of nonlinear wave equations with bilinear control term

Résumé

In this paper we prove that the Ball-Marsden-Slemrod controllability obstruction also holds for nonlinear equations, with integrable bilinear controls. We first show an abstract result and then we apply it to nonlinear wave equations. The first application to the Sine-Gordon equation directly follows from the abstract result, and the second application concerns the cubic wave/Klein-Gordon equation and needs some additional work.
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Dates et versions

hal-01876952 , version 1 (19-09-2018)
hal-01876952 , version 2 (08-01-2019)
hal-01876952 , version 3 (01-05-2019)

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Thomas Chambrion, Laurent Thomann. A topological obstruction to the controllability of nonlinear wave equations with bilinear control term. SIAM Journal on Control and Optimization, 2019, 57 (4), pp.2315-2327. ⟨10.1137/18M1215207⟩. ⟨hal-01876952v3⟩
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