Finite time blow-up for a thin-film equation with initial data at arbitrary energy level

Sun, F.; Liu, Lishan; Wu, Yong Hong

doi:10.1016/j.jmaa.2017.08.047

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Authors

Sun, F.

Liu, Lishan

Wu, Yong Hong

Date

2018

Type

Journal Article

Metadata

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Citation

Sun, F. and Liu, L. and Wu, Y.H. 2018. Finite time blow-up for a thin-film equation with initial data at arbitrary energy level. Journal of Mathematical Analysis and Applications. 458 (1): pp. 9-20.

Source Title

Journal of Mathematical Analysis and Applications

DOI

10.1016/j.jmaa.2017.08.047

ISSN

0022-247X

School

School of Electrical Engineering, Computing and Mathematical Science (EECMS)

URI

http://hdl.handle.net/20.500.11937/62532

Collection

Curtin Research Publications

Abstract

© 2017 In this paper, we consider the initial boundary value problem for a class of thin-film equations in R n with a p-Laplace term and a nonlocal source term |u| q-2 u-[Formula presented]? O |u| q-2 udx. We prove that there exist weak solutions for the problem with arbitrarily initial energy that blow up in finite time. We also obtain the upper bounds for the blow-up time.