Two-phase eigenvalue problem on thin domains with Neumann boundary condition

2017/06/15 by Toshiaki Yachimura, Yachimura, Toshiaki · 1 citation
Computer Science · Engineering · Mathematics · #35J20 #35P20 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #math.SP #msc:35J20 #msc:35P20

paper · pdf · doi:10.48550/arxiv.1706.05027

23 pages, 1 figure

openalex publication_date 2017/06/15 · arxiv created 2020/06/09 · arxiv updated 2020/06/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we study an eigenvalue problem with piecewise constant coefficients on thin domains with Neumann boundary condition, and we analyze the asymptotic behavior of each eigenvalue as the domain degenerates into a certain hypersurface being the set of discontinuities of the coefficients. We show how the discontinuity of the coefficients and the geometric shape of the interface affect the asymptotic behavior of the eigenvalues by a using variational approach.

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• Navier–Stokes Equations in a Curved Thin Domain, Part II: Global Existence of a Strong Solution

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