A viscous thin-film equation with a singular diffusion

Boundary value problems

Bo Liang¹  Ying Wang¹  Xiting Peng¹  Min Pang¹ 

[1] School of Science, Dalian Jiaotong University, Dalian, P.R. China

关键词: fourth-order parabolic;    thin-film equation;    entropy functional;    singular diffusion;   

DOI  :  10.1186/s13661-016-0651-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The paper is devoted to studying a viscous thin-film equation with a singular diffusion term and the periodic boundary conditions in multidimensional space, which has a lot of applications in fluids theory such as draining of foams and the movement of contact lenses. In order to obtain the necessary uniform estimates and overcome the difficulty of a singular diffusion term, the entropy functional method is used. Finally, the existence of nonnegative weak solutions is obtained by some compactness arguments.

【 授权许可】

CC BY