## MOVCOL4: A Moving Mesh Code for Fourth-Order Time-Dependent Partial Differential Equations

- Robert D. Russell, J. F. Williams, Xiaowei Xu
- SIAM J. Scientific Computing
- 2007

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@inproceedings{Brenner1993LossAG, title={Loss and Gain of Regularity in a Lubrication Equation for Thin Viscous Lms}, author={Michael B Brenner and Todd Dupont and Leo Kadano}, year={1993} }

- Published 1993

Fourth order degenerate diiusion equations arise in the motion of thin lms and membranes of viscous liquid in which the surface tension of the liquid/air interface determines the evolution. These equations are derived via a lubrication approximation in which the uid velocity is depth averaged in the direction transverse to the lm 16, 14]. One typically obtains an evolution equation for the thickness h of the lm of the form h t + r (h n rh) = 0; x 2 R d h(x; 0) = h 0 (x) n > 0 (1) where nâ€¦Â CONTINUE READING

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