# Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms

## TL;DR

This paper investigates the long-term behavior of solutions to a level-set mean curvature flow equation with additional driving and source terms, providing convergence results and analyzing a related stationary problem, including a viscosity-based Alexandrov's theorem in 2D.

## Contribution

It offers new convergence results for the asymptotic behavior of the flow and establishes a viscosity version of Alexandrov's theorem in two dimensions.

## Key findings

- Solutions converge to stationary states under certain conditions
- Detailed analysis of the stationary problem in a specific case
- Viscosity Alexandrov's theorem proved in 2D

## Abstract

We study a level-set mean curvature flow equation with driving and source terms, and establish convergence results on the asymptotic behavior of solutions as time goes to infinity under some additional assumptions. We also study the associated stationary problem in details in a particular case, and establish Alexandrov's theorem in two dimensions in the viscosity sense, which is of independent interest.