Volume 32, Issue 4
General Energy Decay of Solutions for a Wave Equation with Nonlocal Damping and Nonlinear Boundary Damping

J. Part. Diff. Eq., 32 (2019), pp. 369-380.

Published online: 2020-01

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• Abstract

In this paper, we consider a nonlinear wave equation with nonlocal damping and nonlinear boundary damping. We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping by using of the multiplier technique from the idea of Martinez [1]. Our result extends and improves the result in the literature such as the work by Lourêdo, Ferreira de Araújo and Mirandain [2] in which only exponential energy decay is considered. Furthermore, we get also the energy decay for the equation with nonlocal damping only but without nonlinear boundary damping.

• Keywords

Wave equation general decay nonlocal damping boundary damping.

35B40, 35L05, 35Q40, 35L20

jiehao1021@163.com (Donghao Li)

whz661@163.com (Hongwei Zhang)

slxhqy@163.com (Qingying Hu)

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@Article{JPDE-32-369, author = {Li , Donghao and Zhang , Hongwei and Hu , Qingying}, title = {General Energy Decay of Solutions for a Wave Equation with Nonlocal Damping and Nonlinear Boundary Damping}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {32}, number = {4}, pages = {369--380}, abstract = {

In this paper, we consider a nonlinear wave equation with nonlocal damping and nonlinear boundary damping. We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping by using of the multiplier technique from the idea of Martinez [1]. Our result extends and improves the result in the literature such as the work by Lourêdo, Ferreira de Araújo and Mirandain [2] in which only exponential energy decay is considered. Furthermore, we get also the energy decay for the equation with nonlocal damping only but without nonlinear boundary damping.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n4.6}, url = {http://global-sci.org/intro/article_detail/jpde/13615.html} }
TY - JOUR T1 - General Energy Decay of Solutions for a Wave Equation with Nonlocal Damping and Nonlinear Boundary Damping AU - Li , Donghao AU - Zhang , Hongwei AU - Hu , Qingying JO - Journal of Partial Differential Equations VL - 4 SP - 369 EP - 380 PY - 2020 DA - 2020/01 SN - 32 DO - http://doi.org/10.4208/jpde.v32.n4.6 UR - https://global-sci.org/intro/article_detail/jpde/13615.html KW - Wave equation KW - general decay KW - nonlocal damping KW - boundary damping. AB -

In this paper, we consider a nonlinear wave equation with nonlocal damping and nonlinear boundary damping. We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping by using of the multiplier technique from the idea of Martinez [1]. Our result extends and improves the result in the literature such as the work by Lourêdo, Ferreira de Araújo and Mirandain [2] in which only exponential energy decay is considered. Furthermore, we get also the energy decay for the equation with nonlocal damping only but without nonlinear boundary damping.

Donghao Li , Hongwei Zhang & Qingying Hu . (2020). General Energy Decay of Solutions for a Wave Equation with Nonlocal Damping and Nonlinear Boundary Damping. Journal of Partial Differential Equations. 32 (4). 369-380. doi:10.4208/jpde.v32.n4.6
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