Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media

In this paper, we study optimization of the first eigenvalue of the heat equation with spatially nonuniform conductivity on a bounded domain under several constraints for the conductivity. We consider this problem in various boundary conditions and various type of topology of domains. As a result, we numerically observe several common criteria of the conductivity for optimizing eigenvalues in terms of corresponding eigenfunctions, which are independent of topology of domains and boundary conditions. The geometric characterization of optimizers are also numerically observed.