Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension
Analysis of PDEs
2020-06-16 v2 Optimization and Control
Abstract
In this paper, we consider a parabolic PDE on a torus of arbitrary dimension. The nonlinear term is a smooth function of polynomial growth of any degree. In this general setting, the corresponding Cauchy problem is not necessarily well posed. We show that the equation in question is approximately controllable by only a finite number of Fourier modes. This result is proved by using some ideas from the geometric control theory introduced by Agrachev and Sarychev.
Keywords
Cite
@article{arxiv.1901.04890,
title = {Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension},
author = {Vahagn Nersesyan},
journal= {arXiv preprint arXiv:1901.04890},
year = {2020}
}