具非局部非线性阻尼和源项的波方程解的能量衰减估计

doi:10.13371/j.cnki.chin.q.j.m.2020.03.005

数学季刊 ›› 2020, Vol. 35 ›› Issue (3): 302-310.doi: 10.13371/j.cnki.chin.q.j.m.2020.03.005

具非局部非线性阻尼和源项的波方程解的能量衰减估计

Department of Mathematics, Henan University of Technology

收稿日期:2020-05-16 出版日期:2020-09-30 发布日期:2020-10-22
作者简介:ZHANG Hongwei(1966-), male, native of Fugou, Henan, professor, Ph.D., engages in PDE.
基金资助:
Supported by National Natural Science Foundation of China(11601122,11801145)；

General Energy Decay of Solutions for A Wave Equation with Nonlocal Nonlinear Damping and Source Terms

Department of Mathematics, Henan University of Technology

Received:2020-05-16 Online:2020-09-30 Published:2020-10-22
About author:ZHANG Hongwei(1966-), male, native of Fugou, Henan, professor, Ph.D., engages in PDE.
Supported by:
Supported by National Natural Science Foundation of China(11601122,11801145)；

摘要/Abstract

摘要： We consider a wave equation with nonlocal nonlinear damping and source terms. We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique. The main difficult is how to handle with the nonlocal nonlinear damping term. Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso（Evolution Equation and Control Theory, 2017（6）:437-470） and Narciso（Evolution Equations and Control Theory, 2020, 9（2）: 487-508）.

关键词: Wave equation, Initial boundary value problem, Nonlinear nonlocal damping, Energy decay

Abstract: We consider a wave equation with nonlocal nonlinear damping and source terms. We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique. The main difficult is how to handle with the nonlocal nonlinear damping term. Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso（Evolution Equation and Control Theory, 2017（6）:437-470） and Narciso（Evolution Equations and Control Theory, 2020, 9（2）: 487-508）.

Key words: Wave equation, Initial boundary value problem, Nonlinear nonlocal damping, Energy decay

中图分类号:

O175.2

张宏伟, 李栋浩, 呼青英. 具非局部非线性阻尼和源项的波方程解的能量衰减估计[J]. 数学季刊, 2020, 35(3): 302-310.

ZHANG Hong-wei, LI Dong-hao, HU Qing-ying. General Energy Decay of Solutions for A Wave Equation with Nonlocal Nonlinear Damping and Source Terms[J]. Chinese Quarterly Journal of Mathematics, 2020, 35(3): 302-310.

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具非局部非线性阻尼和源项的波方程解的能量衰减估计

General Energy Decay of Solutions for A Wave Equation with Nonlocal Nonlinear Damping and Source Terms

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