期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 110, 期 -, 页码 141-156出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2014.08.004
关键词
Nonlocal parabolic equation; Potential well method; Global existence; Blow up
资金
- National Natural Science Foundation of China [11201025, 11271111]
- Doctoral Program Foundation of the Ministry of Education of China [20090002110019]
- Fundamental Research Funds for the Central Universities [FRF-BR-13-023, FRF-TP-12-106A]
In this paper, we consider a nonlocal equation of parabolic type on a bounded smooth domain with Dirichlet boundary condition. First, the well-posedness in Lebesgue spaces is established by using the Banach fixed point theorem. Then we set up the regularity of the solution. More interestingly, we find the invariant sets for the initial boundary value problem and derive a threshold of blow up and global existence for its solution. (C) 2014 Elsevier Ltd.
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