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

作者：Hao, Aijing; Zhou, Jun^*

来源：Journal of Mathematical Analysis and Applications, 2017, 449(1): 897-906.

DOI：10.1016/j.jmaa.2016.12.040

• Parabolic equation with singular potential
• Blow-up
• Nehari manifold

This paper is aimed at giving a new blow-up condition of the following parabolic problem with singular potential
vertical bar x vertical bar(-s)u(t) - Delta u = vertical bar u vertical bar(p-2)u,
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(u(0)) >= 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(u(0)) < d was considered.

• 出版日期2017-5-1
• 单位西南大学