Application of the exact null controllability of the heat equation to moving sets

We study the lagrangian controllability of the heat equation in several dimensions. In dimension one, we prove that any pairs of intervals are diffeomorphic through the flow of the solution of the heat equation via an adequate control. In higher dimensions we prove a similar controllability result for the flow of the gradient of the solution in a radial case in arbitrary finite time, and for convex domains in a sufficiently large time. To cite this article: T. Horsin Molinaro, C. R. Acad. Sci. Paris, Ser. I 342 (2006).