薄膜方程的不变量频域

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-03-25 DOI:10.1007/s00205-024-01968-y

Christian Seis, Dominik Winkler

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引用次数: 0

摘要

摘要研究了在\(\mathbb {R}^N\) 上完全润湿状态下具有线性迁移率的薄膜方程解的大时间行为。我们研究了在初始数据的某些对称性假设下，向自相似 Smyth-Hill 解收敛的解的高阶渐近性。分析基于有限维不变流形的构造，解近似于任意规定阶。

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Invariant Manifolds for the Thin Film Equation

The large-time behavior of solutions to the thin film equation with linear mobility in the complete wetting regime on \(\mathbb {R}^N\) is examined. We investigate the higher order asymptotics of solutions converging towards self-similar Smyth–Hill solutions under certain symmetry assumptions on the initial data. The analysis is based on a construction of finite-dimensional invariant manifolds that solutions approximate to an arbitrarily prescribed order.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.