English

Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and application to controllability

Optimization and Control 2012-11-12 v1 Analysis of PDEs

Abstract

In the discrete setting of one-dimensional finite-differences we prove a Carleman estimate for a semi-discretization of the parabolic operator tx(cx)\partial_t-\partial_x (c\partial_x) where the diffusion coefficient cc has a jump. As a consequence of this Carleman estimate, we deduce consistent null-controllability results for classes of semi-linear parabolic equations.

Keywords

Cite

@article{arxiv.1211.2061,
  title  = {Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and application to controllability},
  author = {Thuy Nguyen},
  journal= {arXiv preprint arXiv:1211.2061},
  year   = {2012}
}