English

The Free Material Design problem for stationary heat equation on low dimensional structures

Analysis of PDEs 2023-07-26 v1 Optimization and Control

Abstract

For a given balanced distribution of heat sources and sinks, QQ, we find an optimal conductivity tensor field, C^\hat C, minimizing the thermal compliance. We present C^\hat C in a rather explicit form in terms of the datum. Our solution is in a cone of non-negative tensor-valued finite Borel measures. We present a series of examples with explicit solutions.49J20, %Singular parabolic equations secondary: 49K20, 80M50

Keywords

Cite

@article{arxiv.2109.14393,
  title  = {The Free Material Design problem for stationary heat equation on low dimensional structures},
  author = {Tomasz Lewiński and Piotr Rybka and Anna Zatorska-Goldstein},
  journal= {arXiv preprint arXiv:2109.14393},
  year   = {2023}
}
R2 v1 2026-06-24T06:28:46.786Z