Stability of self-similar solutions to geometric flows

Interfaces and free boundaries

article

Hengrong Du¹  Nung Kwan Yip² 

[1] Vanderbilt University;Purdue University

关键词: Self-similar solutions;    geometric flows;    mean curvature;   

DOI  :  10.4171/ifb/488

学科分类：生物化学工程

来源: European Mathematical Society

【 摘 要 】

We show that self-similar solutions for the mean curvature flow, surface diffusion, and Willmore flow of entire graphs are stable upon perturbations of initial data with small Lipschitz norm. Roughly speaking, the perturbed solutions are asymptotically self-similar as time tends to infinity. Our results are built upon the global analytic solutions constructed by Koch and Lamm in 2012, the compactness arguments adapted by Asai and Giga in 2014, and the spatial equi-decay properties on certain weighted function spaces. The proof for all of the above flows are achieved in a unified framework by utilizing the estimates of the linearized operator.

【 授权许可】

CC BY