描述外延生长的指数PDE解的全局稳定性

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2018-05-06 DOI:10.4171/IFB/417

Jian‐Guo Liu, Robert M. Strain

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引用次数: 20

摘要

本文证明了指数函数PDE $h_t=\Delta e^{-\Delta h}$在整个空间$\mathbb{R}^d_x$上的全局存在性、唯一性、最优大时间衰减率和均匀可解析性增益。我们假设初始数据在临界维纳代数$\Delta h \in A(\mathbb{R}^d)$中具有中等大小。指数偏微分方程是由(Krug, Dobbs, and Majaniemi, 1995)和(Marzuola and Weare, 2013)导出的。

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Global stability for solutions to the exponential PDE describing epitaxial growth

In this paper we prove the global existence, uniqueness, optimal large time decay rates, and uniform gain of analyticity for the exponential PDE $h_t=\Delta e^{-\Delta h}$ in the whole space $\mathbb{R}^d_x$. We assume the initial data is of medium size in the critical Wiener algebra $\Delta h \in A(\mathbb{R}^d)$. This exponential PDE was derived in (Krug, Dobbs, and Majaniemi in 1995) and more recently in (Marzuola and Weare 2013).

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来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.