期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 458, 期 1, 页码 9-20出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2017.08.047
关键词
Thin-film equation; Blow-up; Upper bound for blow-up time; Arbitrary initial energy; Nonlocal source
资金
- National Natural Science Foundation of China [11371221, 11571296]
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 vertical bar u vertical bar(q-2)u - 1/vertical bar Omega vertical bar integral(Omega) vertical bar u vertical bar(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. Crown Copyright (C) 2017 Published by Elsevier Inc. All rights reserved.
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