Existence and stability of time periodic solutions to nonlinear elastic wave equations with viscoelastic terms

被引：0
作者：
Kagei, Yoshiyuki [1 ,3 ]
Takeda, Hiroshi [2 ]
机构：
[1] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528551, Japan
[2] Fukuoka Univ, Fac Sci, Dept Appl Math, Jonan Ku, Fukuoka 8140180, Japan
[3] Inst Sci Tokyo, Dept Math, Meguro Ku, Tokyo 1528551, Japan
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2025年 / 427卷
关键词：
Nonlinear elastic wave equation; Damping terms; Time periodic solution; Stability; GLOBAL EXISTENCE; DECAY;
D O I：
10.1016/j.jde.2025.01.092
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper studies a nonlinear viscoelastic equation with a time periodic external force on the three dimensional whole space. The existence of a time periodic solution is proved by using a spectral decomposition and the Poincar & eacute; map when the external force is small enough. Based on the regularity estimates of the time periodic solution derived from the smoothing effect of the semigroup, a stability result is obtained with time decay estimates of perturbations. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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页码：478 / 509
页数：32
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