Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations
Analysis of PDEs
2024-02-29 v1 Functional Analysis
Abstract
We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states.
Cite
@article{arxiv.2402.18572,
title = {Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations},
author = {Elie Abdo and Fizay-Noah Lee},
journal= {arXiv preprint arXiv:2402.18572},
year = {2024}
}