Math @ Duke

Publications [#325701] of JianGuo Liu
Papers Published
 Liu, JG; Wang, J, Global existence for a thin film equation with subcritical mass,
Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 4
(June, 2017),
pp. 14611492, American Institute of Mathematical Sciences (AIMS) [doi]
(last updated on 2019/06/19)
Abstract: In this paper, we study existence of global entropy weak solutions to a criticalcase unstable thin film equation in onedimensional case ht + x(hn xxxh) + x(hn+2xh) = 0; where n 1. There exists a critical mass Mc = 2 p 6 3 found by Witelski et al. (2004 Euro. J. of Appl. Math. 15, 223256) for n = 1. We obtain global existence of a nonnegative entropy weak solution if initial mass is less than Mc. For n 4, entropy weak solutions are positive and unique. For n = 1, a finite time blowup occurs for solutions with initial mass larger than Mc. For the Cauchy problem with n = 1 and initial mass less than Mc, we show that at least one of the following longtime behavior holds: the second moment goes to infinity as the time goes to infinity or h(tk) 0 in L1(R) for some subsequence tk 1.


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