Numerical null controllability of semi-linear 1-D heat equations : fixed point , least squares and Newton methods

@inproceedings{FernndezCara2011NumericalNC,
title={Numerical null controllability of semi-linear 1-D heat equations : fixed point , least squares and Newton methods},
author={Enrique Fern{\'a}ndez-Cara and Arnaud M{\"u}nch},
year={2011}
}

This paper deals with the numerical computation of distributed null controls for semilinear 1D heat equations, in the sublinear and slightly superlinear cases. Under sharp growth assumptions, the existence of controls has been obtained in [Fernandez-Cara & Zuazua, Null and approximate controllability for weakly blowing up semi-linear heat equation, 2000] via a fixed point reformulation; see also [Barbu, Exact controllability of the superlinear heat equation, 2000]. More precisely, Carleman… CONTINUE READING