Researcher Information

JIMBO Shuichi

Professor

Look into the solution space of PDEs in a complex domain

Department of Mathematics, Mathematics

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Theme

Analysis on PDEs in a complicated or extreme domain as an application of the spectral theory.

FieldPartial differential equations, Applied analysis
KeywordSpectral analysis, Elliptic equations, Complex domains, Singular perturbation problems

Introduction of Research

Solutions and their structure of a PDE strongly depend on the geometry of the domain. Such kind of idea of research arose in the work of Hadamard of a hundred years ago. He studied the variation of the eigenvalues and Green function of the Laplacian when the domain is smoothly deformed (Hadamard variation). In Physical phenomena such as light and sound or vibration of material, important feature (spectra, frequencies) depend on the shape of the space of phenomena. Mathematically, they are problems of analysis of the relation between geometry and the solution structure of PDEs. Recently I am studying the spectral problem of the Stokes equation for fluid mechanics and the Lame system of elastic body oscillation in relation with the shape of the space. The method developed in my research work is expected to be applicable to other problems of equations of material sciences.

Representative Achievements

Asymptotic behavior of eigenfrequencies of a thin elastic rod with non-uniform cross-section,
S. Jimbo and A. Rodrigues Mulet, J. Math. Soc. Japan. 72 (2020), 119-154.
Entire solutions to reaction-diffusion equations in multiple half-lines with a junction,
S. Jimbo and Y. Morita, J. Differential Equations, 267 (2019), 1247-1276.
Eigenvalues of the Laplacian in a domain with a thin tubular hole,
S. Jimbo, J. Elliptic, Parabolic Equations 1 (2015), 137-174
Spectra of domains with partial degeneration,
S. Jimbo and S. Kosugi, J. Math. Sci. Univ. Tokyo, 16 (2009), 269-414.
Ginzburg-Landau equation and stable solutions in a nontrivial domain,
S. Jimbo, Y. Morita, J. Zhai, Comm. Partial Differential Equations 20 (1995), 2093-2112.
Academic background1981 Bachelor of the University of Tokyo
1983 Master of the University of Tokyo
1987 Doctor of the University of Tokyo
1987 Assistant professor of the University of Tokyo
1990 Lecturer of Okayama university
1992 Associate professor of Okayama University
1993 Associate professor of Hokkaido university
1999 Professor of Hokkaido university
Affiliated academic societyMathematical Society of Japan
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