Dynamics of strongly damped wave equations in locally uniform spaces: Attractors and asymptotic regularity
Dynamics of strongly damped wave equations in locally uniform spaces: Attractors and asymptotic regularity
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DOI：
10.1090/s0002-9947-08-04680-1
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发表时间：
2008-09
影响因子：
1.3
通讯作者：
Meihua Yang;Chunyou Sun
中科院分区：
文献类型：
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作者：
Meihua Yang;Chunyou Sun
本文研究了具有临界非线性的强阻尼波方程在局部一致空间中的动力学行为。在证明了全局适定性之后，我们首先建立了最优解的渐近正则性和关于H_1lu(R_N)x L 2_lu(R_N)-范数指数地吸引每个初始H_1lu(R_N)×L 2_lu(R_N)-有界集的有界子集的存在性。然后证明了存在一个(H1lu(RN)x L 2lu(RN)，H1ρ(RN)xH1ρ(RN))-整体吸引子，它在一定程度上反映了Δutt的强阻尼性.
This paper is dedicated to analyzing the dynamical behavior of strongly damped wave equations with critical nonlinearity in locally uniform spaces. After proving the global well-posedness, we first establish the asymptotic regularity of the solutions which appears to be optimal and the existence of a bounded (in H 2 lu (R N ) x H 1 lu (R N )) subset which attracts exponentially every initial H 1 lu (R N ) x L 2 lu (R N )-bounded set with respect to the H 1 lu (R N ) x L 2 lu (R N )-norm. Then, we show there is a (H 1 lu (R N ) x L 2 lu (R N ), H 1 ρ (R N ) x H 1 ρ (R N ))-global attractor, which reflects the strongly damped property of Δu t to some extent.