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

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

References in corpus (2)

• Some results on Sobolev spaces with respect to a measure and applications to a new transport problem
• Optimal design versus maximal Monge-Kantorovich metrics