THIN FILM FLOW DYNAMICS ON FIBER NETS

被引：1

作者：

Taranets, Roman M. ^{[1
]}

Chugunova, Marina ^{[2
]}

机构：

[1] NASU, Inst Appl Math & Mech, 1 Dobrovolskogo Str, UA-84100 Sloviansk, Ukraine

[2] Claremont Grad Univ, Inst Math Sci, 150 E 10th Str, Claremont, CA 91711 USA

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2018年 / 16卷 / 03期

关键词：

thin film equation; graph theory; steady states; existence of weak solutions; energy method; entropy estimates; Galerkin method; PARABOLIC EQUATIONS; GRAPHS; NETWORKS; MODELS;

D O I：

10.4310/CMS.2018.v16.n3.a7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze existence and qualitative behavior of non-negative weak solutions for fourth order degenerate parabolic equations on graph domains with Kirchhoff's boundary conditions at the inner nodes and Neumann boundary conditions at the boundary nodes. The problem is originated from industrial constructions of spray coated meshes which are used in water collection and in oil-water separation processes. For a certain range of parameter values we prove convergence toward a constant steady state that corresponds to the uniform distribution of coating on a fiber net.

引用

页码：763 / 775

页数：13

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