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arXiv · 2109.14393

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

Tomasz Lewiński·Piotr Rybka·Anna Zatorska-Goldstein
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Abstract

For a given balanced distribution of heat sources and sinks, $Q$, we find an optimal conductivity tensor field, $\hat C$, minimizing the thermal compliance. We present $\hat C$ 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

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Tomasz Lewiński, Piotr Rybka, Anna Zatorska-Goldstein. 2021-09-29. The Free Material Design problem for stationary heat equation on low dimensional structures. https://doi.org/10.1088/1361-6544/ace303

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