The Moore-Gibson-Thompson equation with memory in the critical case
The Moore-Gibson-Thompson equation with memory in the critical case
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DOI：
10.1016/j.jde.2016.06.025
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发表时间：
2016-10-05
影响因子：
2.4
通讯作者：
Pata, Vittorino
中科院分区：
文献类型：
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作者：
Dell'Oro, Filippo;Lasiecka, Irena;Pata, Vittorino
我们考虑具有记忆偏导数（ttt）u（t）+ α偏导数（tt）u（t）+ β A偏导数（t）u（t）+ γ Au（t）-积分（t）g（s）Au（t-s）ds = 0的Moore-Gibson-Thompson方程的以下抽象形式，取决于参数α，β，γ> 0，其中A是严格正自伴线性算子，g是凸（非负）记忆核。在亚临界情况下，α β> γ，相关能量已在[19]中显示为指数衰减。在这里，我们讨论的关键情况下，α β = γ，我们证明了指数稳定性发生当且仅当A是一个有界算子。尽管如此，当A也是无界的时，能量衰减到零。(C)2016 Elsevier Inc. All rights reserved.
We consider the following abstract version of the Moore-Gibson-Thompson equation with memorypartial derivative(ttt)u(t) + alpha partial derivative(tt)u(t) + beta A partial derivative(t)u(t) + gamma Au(t) - integral(t) g(s)Au(t - s)ds = 0depending on the parameters alpha, beta, gamma > 0, where A is strictly positive selfadjoint linear operator and g is a convex (nonnegative) memory kernel. In the subcritical case alpha beta > gamma, the related energy has been shown to decay exponentially in [19]. Here we discuss the critical case alpha beta = gamma, and we prove that exponential stability occurs if and only if A is a bounded operator. Nonetheless, the energy decays to zero when A is unbounded as well. (C) 2016 Elsevier Inc. All rights reserved.