The cost of the control in the case of a minimal time of control: the example of the one-dimensional heat equation
Lissy, Pierre (2017), The cost of the control in the case of a minimal time of control: the example of the one-dimensional heat equation, Journal of Mathematical Analysis and Applications, 451, 1, p. 497-507. 10.1016/j.jmaa.2017.01.096
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Analysis and Applications
MetadataShow full item record
Abstract (EN)In this article, we consider the controllability of the one-dimensional heat equation with an internal control depending only on the time variable and an imposed profile depending on the space variable. It is well-known that in this context, there might exist a minimal time of null-controllability T0, depending on the behavior of the Fourier coefficients of the profile. We prove two different results. The first one, which is surprising, is that the cost of the controllability in time T > T0 close to T0 may explode in an arbitrary way. On the other hand, we prove as a second result that for a large class of profiles, the cost of controllability at time T > T0 is bounded from above by exp(C(T0)/(T − T0)) for some constant C(T0) > 0 depending on T0. The main method used here is the moment method and some tools coming from complex analysis.
Subjects / Keywordsnon-harmonic Fourier series; minimal time; controllability cost; null controllability; parabolic equations; moment method
Showing items related by title and author.
Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using a finite-difference method Lissy, Pierre; Roventa, Ionel (2019) Article accepté pour publication ou publié
A geometric theory forL 2-stability of the inverse problem in a one-dimensional elliptic equation from anH 1-observation Chavent, Guy; Kunisch, Karl (1993) Article accepté pour publication ou publié
Explicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport–diffusion equation Lissy, Pierre (2015) Article accepté pour publication ou publié
Guerrero, Sergio; Glass, Olivier; Puel, Jean-Pierre; Ervedoza, Sylvain (2012) Article accepté pour publication ou publié