Weak Solution of a Doubly Degenerate Parabolic Equation [article]

Di Kang, Tharathep Sangsawang, Jialun Zhang
2017 arXiv   pre-print
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.
arXiv:1610.06303v2 fatcat:d2bv63ybunhw7okgfau6xwl3nu