Geometric PDE and Applied Analysis Seminar (October 24, 2024)

Talk 1: 15:00-16:00

Speaker: Prof. Jun-ichi Segata (Kyushu University)

Title: Scattering problem for the generalized Korteweg-de Vries equation

Abstract: In this talk, we study the scattering problem for the initial value problem of the generalized Korteweg-de Vries (gKdV) equation. The purpose of this talk is to achieve two primary goals. Firstly, we show small data scattering for (gKdV) in the weighted Sobolev space, ensuring the initial and the asymptotic states belong to the same class. Secondly, we introduce two equivalent characterizations of scattering in the weighted Sobolev space. In particular, this involves the so-called conditional scattering in the weighted Sobolev space. This talk is based on a joint work with Satoshi Masaki (Hokkaido University).

Talk 2: 16:15-17:15

Speaker: Prof. Takashi Kagaya (Muroran Institute of Technology)

Title: Sharp interface limit for a large deviation rate function

Abstract: In this talk, we discuss on the singular limit problem for a functional motivated by large deviation theory. A property of the functional is that its minimum solution is a solution of the Allen-Cahn equation. It is known that the solution of the Allen-Cahn equation generate a sharp interface which move along with the mean curvature equation as an approximate parameter tends to 0. For the functional, we will consider a formal gamma convergence related to the sharp interface limit. This talk is based on a joint work with Prof. Kenkichi Tsunoda (Kyushu University).