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, , we find an optimal conductivity tensor field, , minimizing the thermal compliance. We present 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}
}