Upper semicontinuity of pullback attractors for lattice nonclassical diffusion delay equations under singular perturbations
Upper semicontinuity of pullback attractors for lattice nonclassical diffusion delay equations under singular perturbations
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DOI：
10.1016/j.amc.2014.05.045
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
Meiyu Sui;Yejuan Wang
中科院分区：
文献类型：
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作者：
Meiyu Sui;Yejuan Wang
我们考虑以下的晶格非经典扩散方程，它具有延迟v i (t)+ λ 0 v i (t)+(-1) p Δ p v i (t)+ ε (-1) p Δ p v i (t)= f i (v i (t-ρ (t)) + g i (t), i∈Z，其中ε∈(0,1)，λ 0是λ 0< 1的正常数，p是任意正整数，而接收者为离散一维拉普拉斯算子。在f和g上的适当条件下，证明了ε-小摄动系统的多值过程解的唯一性不需要成立的回拉吸引子的存在性。此外，我们还比较了原始系统和ε-小摄动系统的动力学特性，表明它们的吸引子在Hausdorff半距离意义上是“接近”的。
We consider the following lattice nonclassical diffusion equation with delays v ̇ i (t)+ λ 0 v i (t)+(-1) p Δ p v i (t)+ ε (-1) p Δ p v ̇ i (t)= f i (v i (t-ρ (t)))+ g i (t), i∈ Z, where ε∈(0, 1], λ 0 is a positive constant with λ 0< 1, p is any positive integer and▵ is the discrete one-dimensional Laplace operator. Under suitable conditions on f and g we prove the existence of pullback attractors for the multi-valued process associated with the ε-small perturbed systems for which the uniqueness of solutions need not hold. Moreover, we compare the dynamics of the original systems and the ε-small perturbed systems, and show that their attractors are “close” in the sense of Hausdorff semidistance.