一类具对数非线性项的薄膜方程  

A class of thin-film equations with logarithmic nonlinearity

作　　者：韩玉柱[1] 高文杰[1] 石小葳 Yuzhu Han;Wenjie Gao;Xiaowei Shi

机构地区：[1]吉林大学数学学院

出　　处：《中国科学：数学》2019年第12期1765-1778,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11401252);吉林省青年基金(批准号:20160520103JH)资助项目

摘　　要：本文主要研究一类具对数非线性项的薄膜方程初边值问题.首先利用Galerkin逼近得到了弱解的局部存在性;然后借助修正的对数型Sobolev不等式和位势井方法,证明了一定条件下弱解的整体存在性和无穷远处爆破性及整体解的衰减估计.The main purpose of this paper is to study an initial-boundary value problem for a thin-film equation with logarithmic nonlinearity.Local existence of weak solutions is obtained by using Galerkin's approximation.By using the modified logarithmic Sobolev inequality and the potential well method,we obtain the existence of global solutions and solutions that blow up at infinity under some suitable conditions.The decay estimates of the global solutions are also derived.

关 键 词：薄膜方程 对数非线性项 位势井 整体存在 无穷远爆破 

分 类 号：O17[理学—数学]