Vacuum isolating, blow up threshold, and asymptotic behavior of solutions for a nonlocal parabolic equation
Vacuum isolating, blow up threshold, and asymptotic behavior of solutions for a nonlocal parabolic equation
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DOI：
10.1063/1.5004668
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发表时间：
2017-01
影响因子：
1.3
通讯作者：
Xiaoliang Li;Baiyu Liu
中科院分区：
文献类型：
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作者：
Xiaoliang Li;Baiyu Liu
本文研究了一类具有初始边界条件和狄利克雷边界条件的非局部抛物方程。首先，我们借助一组势阱讨论了溶液的真空隔离行为。然后我们得到了全局存在的一个阈值，并对具有临界初始能量的解进行了爆破。进一步，对于满足J(u0)≤d且I(u0)≠0的解，我们证明了随着时间趋于无穷，全局解呈指数衰减为零，爆破解的范数呈指数增长。
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.