TY - JOUR
T1 - Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media
AU - Matsue, Kaname
AU - Naito, Hisashi
N1 - Publisher Copyright:
© 2015, The JJIAM Publishing Committee and Springer Japan.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2015/7/28
Y1 - 2015/7/28
N2 - In this paper, we study optimization of the first eigenvalue of $$-\nabla \cdot (\rho (x) \nabla u) = \lambda u$$-∇·(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.
AB - In this paper, we study optimization of the first eigenvalue of $$-\nabla \cdot (\rho (x) \nabla u) = \lambda u$$-∇·(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.
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U2 - 10.1007/s13160-015-0177-5
DO - 10.1007/s13160-015-0177-5
M3 - Article
AN - SCOPUS:84938196860
VL - 32
SP - 489
EP - 512
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
SN - 0916-7005
IS - 2
ER -