The Inverse Problem of Reconstructing Reaction-Diffusion Systems
Numerical Analysis
2020-08-26 v1 Numerical Analysis
Abstract
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a time trace of their values at a fixed point on the boundary of the spatial domain. We show both uniqueness results and the convergence of an iteration scheme designed to recover these sources. This leads to a reconstructive method and we shall demonstrate its effectiveness by several illustrative examples.
Cite
@article{arxiv.2003.00489,
title = {The Inverse Problem of Reconstructing Reaction-Diffusion Systems},
author = {Barbara Kaltenbacher and William Rundell},
journal= {arXiv preprint arXiv:2003.00489},
year = {2020}
}