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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:458

Article

Sun, Fenglong¹  Liu, Lishan^1,2  Wu, Yonghong² 

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[2] Curtin Univ, Dept Math & Stat, Perth, WA 6845, Australia

关键词: Thin-film equation;    Blow-up;    Upper bound for blow-up time;    Arbitrary initial energy;    Nonlocal source;   

DOI  :  10.1016/j.jmaa.2017.08.047

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free