On asymptotic speed of solutions to level-set mean curvature flow equations with driving and source terms

TL;DR

This paper studies the long-term behavior of solutions to a level-set mean curvature flow equation with additional driving and source terms, revealing new nonlinear phenomena influenced by source shapes.

Contribution

It establishes well-posedness and uncovers a novel nonlinear asymptotic speed behavior sensitive to source term geometries.

Findings

Solutions exhibit a new type of nonlinear asymptotic speed

Asymptotic speed is highly sensitive to source term shapes

Well-posedness of solutions is rigorously proved

Abstract

We investigate a model equation in the crystal growth, which is described by a level-set mean curvature flow equation with driving and source terms. We establish the well-posedness of solutions, and study the asymptotic speed. Interestingly, a new type of nonlinear phenomena in terms of asymptotic speed of solutions appears, which is very sensitive to the shapes of source terms.