Nonlinear Fisher information, corresponding functional inequalities and applications
Analysis of PDEs
2025-09-03 v1
Abstract
We study the evolution of the nonlinear version of the Fisher information along the quasilinear heat equation. We also provide a nonlinear version of a recent functional inequality (Cie\'slak--Fuest--Hajduk--Sier\.z\k{e}ga, 2024), corresponding to the nonlinear heat equation. Next, applications of our version of nonlinear Fisher information to the 1D critical quasilinear fully parabolic Keller--Segel system are given. In particular, the global existence of solutions to the critical nonlinear diffusion/nonlinear sensitivity 1D fully parabolic Keller--Segel system is obtained for certain type of diffusion. Last, but not least, we also study the version of the Fisher information along the -Laplace equation.
Keywords
Cite
@article{arxiv.2509.01475,
title = {Nonlinear Fisher information, corresponding functional inequalities and applications},
author = {Tomasz Cieślak and Kentaro Fujie and Tatsuya Hosono},
journal= {arXiv preprint arXiv:2509.01475},
year = {2025}
}