Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 58, Issue 10, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.5004668
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Funding
- National Natural Science Foundation of China [11671031, 11201025]
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In this paper, we consider a nonlocal parabolic equation associated with initial and Dirichlet boundary conditions. First, we discuss the vacuum isolating behavior of solutions with the help of a family of potential wells. Then we obtain a threshold of global existence and blow up for solutions with critical initial energy. Furthermore, for those solutions that satisfy J(u(0)) <= d and I(u(0)),not equal 0, we show that global solutions decay to zero exponentially as time tends to infinity and the norm of blow-up solutions increases exponentially. Published by AIP Publishing.
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