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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… Click to show full abstract
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(u0)≤d and I(u0)≠0, we show that global solutions decay to zero exponentially as time tends to infinity and the norm of blow-up solutions increases exponentially.
Journal Title: Journal of Mathematical Physics
Year Published: 2017
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