English

On the numerical solution of a time-dependent shape optimization problem for the heat equation

Optimization and Control 2019-06-17 v1

Abstract

This article is concerned with the solution of a time-dependent shape identification problem. Specifically we consider the heat equation in a domain, which contains a time-dependent inclusion of zero temperature. The objective is to detect this inclusion from the given temperature and heat flux at the exterior boundary of the domain. To this end, for a given temperature at the exterior boundary, the mismatch of the Neumann data is minimized. This time-dependent shape optimization problem is then solved by a gradient-based optimization method. Numerical results are presented which validate the present approach.

Keywords

Cite

@article{arxiv.1906.06221,
  title  = {On the numerical solution of a time-dependent shape optimization problem for the heat equation},
  author = {Rahel Brügger and Helmut Harbrecht and Johannes Tausch},
  journal= {arXiv preprint arXiv:1906.06221},
  year   = {2019}
}
R2 v1 2026-06-23T09:53:54.661Z