On Qualitative Behaviour of Solutions to a Thin Film Equation with a Source Term

被引：0

作者：

Chugunova, M. ^{[1
]}

Ruan, Y. ^{[1
]}

Taranets, R. ^{[2
]}

机构：

[1] Claremont Grad Univ, Inst Math Sci, Claremont, CA 91711 USA

[2] Inst Appl Math & Mech NASU, Sloviansk, Ukraine

来源：

JOURNAL OF NONLINEAR SCIENCE | 2021年 / 31卷 / 01期

关键词：

Thin film equation; Source; Higher-order parabolic equation; Interface propagation; Waiting time phenomenon; 35K35; 35K65;

D O I：

10.1007/s00332-020-09662-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study a one-dimensional degenerate fourth-order parabolic equation (a thin-film model) with a source term. We prove existence of generalized weak solutions for the case n>0 and study interface propagation properties like: finite speed propagation and waiting time phenomenon for the case 1<n<2. Our analysis is based on applications of global and local energy-entropy a priori estimates. Also, we illustrate some of our main analytical results by numerical simulations.

引用

页数：23

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