The Lubrication Approximation for Thin Viscous Films : Regularity and Long Time Behavior of Weak Solutionsa

  title={The Lubrication Approximation for Thin Viscous Films : Regularity and Long Time Behavior of Weak Solutionsa},
  author={L. BERTOZZI AND M. PUGHApril},
  • Published 1994
We consider the fourth order degenerate diiusion equation h t = ?r (f(h)rh) in one space dimension. This equation, derived from a `lubrication approximation', models surface tension dominated motion of thin viscous lms and spreading droplets 14]. The equation with f(h) = jhj also models a thin neck of uid in the Hele-Shaw cell 9, 10, 22]. In such problems h(x; t) is the local thickness of the the lm or neck. This paper will consider the properties of weak solutions which are more relevant to… CONTINUE READING
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