A new blow-up condition for a parabolic equation with singular potential

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• 作者：Aijing Hao ^{haoaijing126@126.com} ; Jun Zhou ; ^{jzhouwm@163.com}
• 关键词：Parabolic equation with singular potential ; Blow-up ; Nehari manifold
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：897-906
• 全文大小：303 K
• 卷排序：449

文摘

This paper is aimed at giving a new blow-up condition of the following parabolic problem with singular potential|x|−sut−Δu=|u|p−2u,|x|−sut−Δu=|u|p−2u, which was studied extensively in recent years. By constructing a new functional, we obtain some blow-up conditions which include the possibility of the initial energy J(u0)≥dJ(u0)≥d, where d   is a positive constant which will be given in the main part of this paper. The results of this paper extend previous results where only the case J(u0)<dJ(u0)<d was considered.