Arnaud Münch

TL;DR: In this paper, the authors developed a more involved and less-standard approach which turns out to be more efficient in its computational implementation, and they also developed the numerical version of the so-called transmutation method that allows writing the control of a heat process in terms of the corresponding control of the associated wave process, by means of a 'time convolution' with a one-dimensional controlled fundamental heat solution.

TL;DR: In this article, the numerical computation of distributed null control for semi-linear 1D heat equations, in the sublinear and slightly superlinear cases, under sharp growth assumptions, was studied.

TL;DR: In this article, the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme is studied.

TL;DR: A new semi-discrete model based on the space discretization of the wave equation using a mixed ¯nite element method with two di®erent basis functions for the position and velocity is introduced and the main theoretical result is a uniform observability inequality which allows for a sequence of approximations converging to the minimal L2inorm control of the continuous wave equation.

TL;DR: The asymptotic behavior as $T$ goes to infinity of the solutions of the relaxed problem is studied and it is proved that, for $T $ large enough, the order of lamination is, in fact, of at most $N-1$.