# Global existence for a thin film equation with subcritical mass

Journal Article

In this paper, we study existence of global entropy weak solutions to a critical-case unstable thin film equation in one-dimensional 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, 223-256) for n = 1. We obtain global existence of a non-negative 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 blow-up 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 long-time 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.

### Full Text

### Duke Authors

### Cited Authors

- Liu, JG; Wang, J

### Published Date

- June 1, 2017

### Published In

### Volume / Issue

- 22 / 4

### Start / End Page

- 1461 - 1492

### International Standard Serial Number (ISSN)

- 1531-3492

### Digital Object Identifier (DOI)

- 10.3934/dcdsb.2017070

### Citation Source

- Scopus