EXISTENCE AND GLOBAL ASYMPTOTIC BEHAVIOR OF MILD SOLUTIONS FOR DAMPED ELASTIC SYSTEMS WITH DELAY AND NONLOCAL CONDITIONS

Mei Wei; Yongxiang Li

doi:10.11948/20220189

2023 Volume 13 Issue 2

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Mei Wei, Yongxiang Li. EXISTENCE AND GLOBAL ASYMPTOTIC BEHAVIOR OF MILD SOLUTIONS FOR DAMPED ELASTIC SYSTEMS WITH DELAY AND NONLOCAL CONDITIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 874-892. doi: 10.11948/20220189

Citation:

Mei Wei, Yongxiang Li. EXISTENCE AND GLOBAL ASYMPTOTIC BEHAVIOR OF MILD SOLUTIONS FOR DAMPED ELASTIC SYSTEMS WITH DELAY AND NONLOCAL CONDITIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 874-892. doi: 10.11948/20220189

EXISTENCE AND GLOBAL ASYMPTOTIC BEHAVIOR OF MILD SOLUTIONS FOR DAMPED ELASTIC SYSTEMS WITH DELAY AND NONLOCAL CONDITIONS

Mei Wei^1, ,,
Yongxiang Li¹

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China

Corresponding author: Email: nwnuweimei@126.com(M. Wei)
Fund Project: The authors were supported by National Natural Science Foundation of China (12061062, 11661071) and Graduate Research Support project of Northwest Normal University (2021KYZZ01030)

Abstract

Abstract

In this paper, we are devoted to the study of a class of structural damped elastic systems with delay and nonlocal conditions in Banach space. Firstly, in the sense of compact semigroup, the existence of mild solutions is studied, where the nonlinearity $ f $ and nonlocal function $ g $ satisfy more general growth conditions rather than Lipschitz-type conditions. Secondly, based on a new Gronwall-Bellman type integral inequality with delay, the global asymptotic stability of the mild solution is discussed. At the end, a concrete example of nonlocal damped beam vibration equation is given to illustrate the feasibility and practical application value of our abstract results.
- Elastic systems /
- structural damping /
- nonlocal problem /
- asymptotic stability /
- compact semigroup
MSC: 34G20, 35B40, 47H20, 47J35

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References

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