Global existence of solutions to a tear film model with locally elevated evaporation rates

Yuan Gao Fudan University Hangjie Ji Duke University Jian-Guo Liu Duke University Thomas P. Witelski Duke University

Analysis of PDEs mathscidoc:1702.03001

2017.2
Motivated by a model proposed by Peng et al. [Advances in Coll. and Interf. Sci. 206 (2014)] for break-up of tear films on human eyes, we study the dynamics of a generalized thin film model. The governing equations form a fourth-order coupled system of nonlinear parabolic PDE for the film thickness and salt concentration subject to nonconservative effects representing evaporation. We analytically prove the global existence of solutions to this model with mobility exponents in several different ranges and the results are then validated against PDE simulations. We also numerically capture other interesting dynamics of the model, including finite-time rupture-shock phenomenon due to the instabilities caused by locally elevated evaporation rates, convergence to equilibrium and infinite-time thinning.
global existence, tear film, fourth-order nonlinear partial differential equations, rupture, thin film equation, evaporation, osmolarity, finite-time singularity
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@inproceedings{yuan2017global,
  title={Global existence of solutions to a tear film model with locally elevated evaporation rates},
  author={Yuan Gao, Hangjie Ji, Jian-Guo Liu, and Thomas P. Witelski},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170202225239424217154},
  year={2017},
}
Yuan Gao, Hangjie Ji, Jian-Guo Liu, and Thomas P. Witelski. Global existence of solutions to a tear film model with locally elevated evaporation rates. 2017. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170202225239424217154.
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