In this paper, we study optimization of the first eigenvalue of $$-abla \cdot (\rho (x) abla u) = \lambda u$$-∇·(ρ(x)∇u)=λu in a bounded domain $$\Omega \subset {\mathbb {R}}^n$$Ω⊂Rn under several constraints for the function $$\rho $$ρ. We consider this problem in various boundary conditions and various topologies of domains. As a result, we numerically observe several common criteria for $$\rho $$ρ for optimizing eigenvalues in terms of corresponding eigenfunctions, which are independent of topology of domains and boundary conditions. Geometric characterizations of optimizers are also numerically observed.
CITATION STYLE
Matsue, K., & Naito, H. (2015). Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media. Japan Journal of Industrial and Applied Mathematics, 32(2), 489–512. https://doi.org/10.1007/s13160-015-0177-5
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