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The Free Material Design problem for stationary heat equation on low dimensional structures (2109.14393v1)
Published 29 Sep 2021 in math.AP and math.OC
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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