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

Abstract

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.

13 pages, SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, In press

References in corpus (1)

• Environment-assisted quantum control of a solid-state spin via coherent dark states

Cited by in corpus (3)

• A remark on the attainable set of the Schrödinger equation
• Small-Time Local Controllability of the multi-input bilinear Schrödinger equation thanks to a quadratic term
• Obstruction to the billinear control of the Gross-Pitaevskii equation: an example with an unbounded potential