具非局部非线性阻尼和源项的波方程解的能量衰减估计

张宏伟, 李栋浩, 呼青英

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

数学季刊 >

2020 , Vol. 35 >Issue 3: 302 - 310

DOI: https://doi.org/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

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Department of Mathematics, Henan University of Technology

ZHANG Hongwei(1966-), male, native of Fugou, Henan, professor, Ph.D., engages in PDE.

收稿日期: 2020-05-16

网络出版日期: 2020-10-22

基金资助

Supported by National Natural Science Foundation of China(11601122,11801145)；

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

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Department of Mathematics, Henan University of Technology

ZHANG Hongwei(1966-), male, native of Fugou, Henan, professor, Ph.D., engages in PDE.

Received date: 2020-05-16

Online published: 2020-10-22

Supported by

Supported by National Natural Science Foundation of China(11601122,11801145)；

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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

本文引用格式

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

Abstract

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

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