Weak Solution of a Doubly Degenerate Parabolic Equation
  This paper studies a fourth-order, nonlinear, doubly-degenerate parabolic equation derived from the thin film equation in spherical geometry. A regularization method is used to study the equation and several useful estimates are obtained. The main result of this paper is to prove the existence of a weak solution of the equation in a weighted Sobolev space. 
Di Kang, Tharathep Sangsawang and Jialun Zhang
math.AP