ABSTRACT

In this paper, we consider a wave equation with Wentzell dynamical boundary conditions and internal and boundary delay terms. We have obtained a global existence and energy decay estimates of the solutions to our problem for nonlinear dampings and nonlinear time delay terms. We would like to see the influence of frictional damping on the rate of decay of solutions in the presence of nonlinear delay term. We study the asymptotic behaviour of solutions using a perturbed energy method under some conditions between the weight of delay terms in the feedbacks and the weight of the terms without delay.

中文翻译：

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具有 Wentzell 边界条件和非线性延迟项的波动方程的一般衰减

摘要

在本文中，我们考虑具有 Wentzell 动态边界条件和内部和边界延迟项的波动方程。我们已经获得了非线性阻尼和非线性时延项问题解的全局存在性和能量衰减估计。我们希望看到在存在非线性延迟项的情况下摩擦阻尼对解衰减率的影响。我们在反馈中延迟项的权重与无延迟项的权重之间的某些条件下，使用扰动能量法研究解的渐近行为。