Enhanced dissipation by advection and applications to PDEs

A. L. Mazzucato; Y. Feng; C. Nobili

doi:10.1016/j.apm.2025.116310

Enhanced dissipation by advection and applications to PDEs

A. L. Mazzucato^*
, Y. Feng
, C. Nobili

^*此作品的通讯作者

数学科学学院

Pennsylvania State University
University of Surrey

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

This survey provides a concise yet comprehensive overview on enhanced dissipation phenomena, transitioning seamlessly from the physical principles underlying the interplay between advection and diffusion to their rigorous mathematical formulation and analysis. The discussion begins with the standard theory of enhanced dissipation, highlighting key mechanisms and results, and progresses to its applications in notable nonlinear PDEs such as the Cahn-Hilliard and the Kuramoto-Sivashinsky equations.

源语言	英语
期刊论文编号	116310
期刊	Applied Mathematical Modelling
卷	150
DOI	https://doi.org/10.1016/j.apm.2025.116310
出版状态	已出版 - 2月 2026

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AB - This survey provides a concise yet comprehensive overview on enhanced dissipation phenomena, transitioning seamlessly from the physical principles underlying the interplay between advection and diffusion to their rigorous mathematical formulation and analysis. The discussion begins with the standard theory of enhanced dissipation, highlighting key mechanisms and results, and progresses to its applications in notable nonlinear PDEs such as the Cahn-Hilliard and the Kuramoto-Sivashinsky equations.

KW - Advection

KW - Enhanced dissipation

KW - Hypocoercivity

KW - Nonlinear PDEs

KW - Resolvent estimate

KW - Taylor's dispersion

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Enhanced dissipation by advection and applications to PDEs

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