JIMBO, Shuichi

JIMBO, Shuichi
Research Field
Applied Mathematics
Department of Mathematics
Research Interest
Elliptic and Parabolic PDEs, Domain deformations, spectral Theory, Sungular Perturbation
Research Activities

Singular deformation of domains and spectral analysis: I enjoy walking on mountains in summer and skiing in winter. I walk around the woods, look at trees and feel the atmosphere. It is quite a joyful and comfortable experience. From physical point of view, this can be well simulated and demonstrated by receiving sound waves, light waves or mechanical vibrations induced by natural phenomena. They are the objects which I like to understand very well. These phenomena are written mathematically in terms of PDEs, which are several kinds of wave equations depending on the situations. Elliptic operators appear in these equations. My research interest is to study and analyze the spectra of these operators, centered around their dependence on the geometric properties and several other environment-oriented features.

[1] S. Jimbo and K. Kurata, Asymptotic behavior of eigenvalues of the Laplacian on a thin domain under the mixed boundary condition, Indiana Univ. Math. J. 65 (2016), 867-898.
[2] S. Jimbo, Eigenvalues of the Laplacian in a domain with a thin tubular hole, J. Elliptic Parabolic Equations, 1 (2015), 137-173.
[3] S. Jimbo and S. Kosugi, Spectra of domains with partial degeneration, J. Math. Sci. Univ. Tokyo 16 (2009), 269-414.
[4] S. Jimbo, Y. Morita and J. Zhai, Ginzburg-Landau equation and stable steady state solutions in a non-trivial domain, Comm. PDE 20 (1995),2093-2112.
[5] S. Jimbo, Singular perturbation of domains and the semilinear elliptic equation II, J. Differential Equations 75 (1988), 246-289.
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