New dissipated energy and partial regularity for thin film equations

[摘要] We study the thin film equation h(t) = -(h(n)h(xxx))(x), and prove that the energy integral h(-1)ph(x)(2)dx dissipates for suitable weak solutions when (n, p) lies in the whole domain epsilon defined by Laugesen, which extends partially the corresponding results of Laugesen, Chugunova and Taranets, and then improve some previous results of partial regularity by Chou and the first author. (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Hausdorff dimension;Thin film equation;Rupture set;Partial regularity