Asymptotic behavior of a diffused interface volume-preserving mean curvature flow

TL;DR

This paper studies a diffused interface model of volume-preserving mean curvature flow, proving that solutions exponentially converge to diffused spheres in all dimensions under natural initial conditions.

Contribution

It establishes exponential convergence of the diffused interface volume-preserving mean curvature flow to diffused balls across all dimensions, under natural assumptions.

Findings

Proves exponential convergence to diffused spheres.

Valid in all spatial dimensions.

Operates under natural initial data assumptions.

Abstract

We consider a diffused interface version of the volume-preserving mean curvature flow in the Euclidean space, and prove, in every dimension and under natural assumptions on the initial datum, exponential convergence towards single "diffused balls".