当前位置: X-MOL 学术J. Nonlinear Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On Qualitative Behaviour of Solutions to a Thin Film Equation with a Source Term
Journal of Nonlinear Science ( IF 2.6 ) Pub Date : 2021-01-07 , DOI: 10.1007/s00332-020-09662-5
M. Chugunova , Y. Ruan , R. Taranets

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.



中文翻译:

带有源项的薄膜方程解的质性行为

在本文中,我们研究带有源项的一维简并四阶抛物线方程(薄膜模型)。我们证明了情况\(n> 0 \)的广义弱解的存在,并研究了接口传播特性,例如:情况\(1 <n <2 \)的有限速度传播和等待时间现象。我们的分析是基于对全局和局部能量熵的先验估计。此外,我们通过数值模拟说明了我们的一些主要分析结果。

更新日期:2021-01-07
down
wechat
bug