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

Donghao Li ,  Hongwei Zhang and Qingying Hu

10.4208/jpde.v32.n4.6

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

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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.

  • History

Published online: 2020-01

  • AMS Subject Headings

35B40, 35L05, 35Q40, 35L20

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