Loss and Gain of Regularity in a Lubrication Equation for Thin Viscous Lms

@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}
}
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 n… CONTINUE READING
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