English

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

Optimization and Control 2019-05-03 v3 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.1809.07107,
  title  = {A topological obstruction to the controllability of nonlinear wave equations with bilinear control term},
  author = {Thomas Chambrion and Laurent Thomann},
  journal= {arXiv preprint arXiv:1809.07107},
  year   = {2019}
}

Comments

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