Nonlinear Fisher information and its application to 1D critical quasilinear fully parabolic Keller--Segel system

par Tatsuya Hosono (Chambéry & Osaka)

mercredi 10 déc. 2025, 10:30 → 12:00 Europe/Paris

112 (Braconnier)

In this talk, we investigate the time evolution of Fisher information, which is known as the entropy production, for nonlinear diffusion equations on bounded domains with Neumann boundary conditions, extending classical results for the linear heat equation and the porous medium equation on the whole space. In particular, we introduce an alternative formulation of one-dimensional nonlinear Fisher information that reveals its time monotonicity. As an application, the existence of global solutions to the one-dimensional critical quasilinear fully parabolic Keller--Segel system with nonlinear diffusion and nonlinear sensitivity is studied. This is based on joint work with Tomasz Cieślak (IMPAN, Poland) and Kentaro Fujie (Tohoku University, Japan).