Researcher Information

Shuichi Jimbo

Professor

Looking at solutions of PDE by deforming the domain

Department of Mathematics, Mathematics

basic_photo_1
Theme

Analysis into the spectral structure of elliptic opeatros in a complicated domains

FieldApplied Analysis, Partial Differential Equations
KeywordComplicated domains, Elliptic operator, Spectral Analysis

Introduction of Research

Solutions of partial defferential equations depend on the geometric property of domans. The origin of analysis into such mathematical phenomena is the work of famous Hadamard of 100years ago. He studied the pertubation of the eigenvalue of the Laplacian under deformation of domains. The phenomena of light, sound, vibration of materials depend on the geometric properties of the environment where they occur. I study the mathematical relation and dependence through the elliptic opeators which arise in the model equations of the phenomena.

Representative Achievements

S.Jimbo, Y.Morita, Nonlocal eigenvalue problems arising in a generalized phase-field-type system, Japan J. Indust. Appl. Math. {bf 34} (2017), 555-584
S. Jimbo, Eigenvalues of the Laplacian in a domain with a thin tubular hole, J. Elliptic, Parabolic, Equations 1 (2015),137-174.
S.Jimbo, S. Kosugi, Spectra of domains with partial degeneration, J. Math. Sci. Univ. Tokyo 16 (2009), 269-414.
S.Jimbo, Y. Morita, J. Zhai, Ginzburg-Landau equation and stable solutions in a nontrivial domain, Comm. Partial Differential Equations 20 (1995), 2093-2112
Academic background1981 Bachelor of the Univesity of Tokyo
1983 Master of the Univesity 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