Strong solutions to the Stefan problem with Gibbs-Thomson correction and boundary contact

Stability in the Stefan problem with surface tension (I)

We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension - also known as the Stefan problem with Gibbs-Thomson correction.

2D中一相准稳态Stefan问题的嵌入性丧失

Loss of embeddedness for the one-phase quasistationary Stefan problem in 2D

本文构造了一个光滑且嵌入的初始状态例子，证明其在2D准稳态Stefan问题（含Gibbs-Thomson修正和动力学过冷）下会在有限时间内丧失嵌入性。

Analysis of a mathematical model for tumor growth with Gibbs-Thomson relation

In this paper we study a mathematical model for the growth of nonnecrotic solid tumor. The tumor is assumed to be radially symmetric and its radius R(t) is an unknown function of time t as tumor growth, and the model is in the form of a free boundary problem. The feature of the model is that a Gibbs-Thomson relation is taken into account, which resulting an interesting phenomenon that there exist two stationary solutions (depending on the model parameters). The global existence and uniqueness of solution are established. By denoting c the ratio of the diffusion time scale to the tumor doubling…

Asymptotic behavior of solutions of a free boundary problem modeling tumor spheroid with Gibbs-Thomson relation

In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor, respectively. The new feature is that nutrient concentration on the boundary is less than external supply due to a Gibbs-Thomson relation and the problem has two radial stationary solutions, which differs from widely studied tumor spheroid model with surface tension effect. We first establish local well-posedness by using a functional approach based on Fourier multiplier method and analytic semigr…

Convergence of phase-field approximations to the Gibbs-Thomson law

We prove the convergence of phase-field approximations of the Gibbs-Thomson law. This establishes a relation between the first variation of the Van-der-Waals-Cahn-Hilliard energy and the first variation of the area functional. We allow for folding of diffuse interfaces in the limit and the occurrence of higher-multiplicities of the limit energy measures. We show that the multiplicity does not affect the Gibbs-Thomson law and that the mean curvature vanishes where diffuse interfaces have collided. We apply our results to prove the convergence of stationary points of the Cahn-Hilliard equation t…

Numerical and analytical investigation of the free boundary confluence for the phase field system

In this paper we numerically research the solutions of the phase field system for the spherically symmetric Stefan-Gibbs-Thomson problem in the case of interaction of the free boundaries. We analyze the effect of the soliton type disturbance of the temperature in the point of the contact of the free boundaries.