A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications
Analysis of PDEs
2023-10-03 v1
Abstract
This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of nonlocal Hamilton--Jacobi equations and establish a control-based representation formula for solutions. We also apply the formula to discuss the fattening phenomenon and large-time asymptotics of the solutions.
Keywords
Cite
@article{arxiv.2310.00925,
title = {A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications},
author = {Takashi Kagaya and Qing Liu and Hiroyoshi Mitake},
journal= {arXiv preprint arXiv:2310.00925},
year = {2023}
}
Comments
33 pages