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

Kaname Matsue, Hisashi Naito

Research output: Contribution to journalArticle

### Abstract

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.

Original language English 489-512 24 Japan Journal of Industrial and Applied Mathematics 32 2 https://doi.org/10.1007/s13160-015-0177-5 Published - Jul 28 2015 Yes

### Fingerprint

Heat Diffusion
Inhomogeneous Media
First Eigenvalue
Numerical Study
Topology
Boundary conditions
Optimization
Eigenvalues and eigenfunctions
Eigenfunctions
Bounded Domain
Eigenvalue
Subset
Hot Temperature

### All Science Journal Classification (ASJC) codes

• Engineering(all)
• Applied Mathematics

### Cite this

In: Japan Journal of Industrial and Applied Mathematics, Vol. 32, No. 2, 28.07.2015, p. 489-512.

Research output: Contribution to journalArticle

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