Sur la contrôlabilité approchée de problèmes paraboliques avec phénomènes d'explosion

Abstract

We consider in this Note distributed systems governed by parabolic evolution equations which can blow up in finite time and which are controlled by initial conditions. We study here the following question: can one choose the initial condition in such a way that the solution does not blow up before a given time T and which is, at time T, as close as we wish from a given state ? Some general results along these lines are presented here. The main elements of the proof are given on an example, namely the equation partial derivative y/partial derivative t - Delta y = lambda y(3) = 0, lambda > 0; more general cases being indicated in final remarks.