## JIMBO Shuichi

Professor

### Look into the solution space of PDEs in a complex domain

Department of Mathematics, Mathematics

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

Field | Partial differential equations, Applied analysis |

Keyword | Spectral 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

S. Jimbo and A. Rodrigues Mulet, J. Math. Soc. Japan. 72 (2020), 119-154.

S. Jimbo and Y. Morita, J. Differential Equations, 267 (2019), 1247-1276.

S. Jimbo, J. Elliptic, Parabolic Equations 1 (2015), 137-174

S. Jimbo and S. Kosugi, J. Math. Sci. Univ. Tokyo, 16 (2009), 269-414.

S. Jimbo, Y. Morita, J. Zhai, Comm. Partial Differential Equations 20 (1995), 2093-2112.

Academic background | 1981 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 society | Mathematical Society of Japan |