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.
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页数：23
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