Exponential Attractors for the Sup-Cubic Wave Equation with Nonlocal Damping

被引：0
|
作者：
Zhou, Feng [1 ]
Sun, Ziying [1 ]
Zhu, Kaixuan [2 ]
Mei, Xinyu [3 ]
机构：
[1] China Univ Petr East China, Coll Sci, Qingdao 266580, Peoples R China
[2] Hunan Univ Arts & Sci, Sch Math & Phys Sci, Changde 415000, Peoples R China
[3] Yunnan Univ, Sch Math & Stat, Kunming 650091, Peoples R China
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2024年 / 47卷 / 04期
关键词：
Wave equation; Nonlocal damping; Sup-cubic nonlinearity; Shatah-Struwe solution; Exponential attractor; ENERGY CRITICAL WAVES; LONG-TIME DYNAMICS; GLOBAL ATTRACTORS; UNIFORM ATTRACTORS; SMOOTH ATTRACTORS; STABILITY; EXISTENCE; DECAY;
D O I：
10.1007/s40840-024-01703-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the long-time dynamics of a wave equation with nonlocal weak damping, nonlocal weak anti-damping and sup-cubic nonlinearity. Based on the Strichartz estimates in a bounded domain, we obtain the global well-posedness of the Shatah-Struwe solutions. To overcome the difficulties brought by the nonlinear weak damping term, we present a new-type Gronwall's lemma to obtain the dissipative for the Shatah-Struwe solutions semigroup of this equation. Finally, we establish the existence of a time-dependent exponential attractor with the help of a more general criteria constructed by the quasi-stable technique.
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页数：34
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