a1 School of Mathematical Sciences, Claremont Graduate University, 710 N. College Avenue, Claremont, CA 91711, USA email: firstname.lastname@example.org
The main result of this paper is the proof of uniqueness of non-negative entropy solutions of the thin film equation ht + (|h|n hxxx)x = 0 for < n < 4. The uniqueness proved under assumptions that the initial data satisfy a finite β-entropy condition for some negative enough exponent β and that the solution is locally monotone at the touchdown point. The new dissipated functional recently constructed by Laugesen (Commun. Pure Appl. Anal., 4(3):613–634, 2005) is used to prove an auxiliary energy equality, and then Grönwall's lemma leads to uniqueness.
(Received August 30 2011)
(Revised March 26 2012)
(Accepted March 27 2012)
(Online publication April 16 2012)