变指数非线性粘弹性波动方程的最优能量衰减率

Pub Date : 2023-08-28 DOI:10.58997/ejde.2023.53

M. I. Mustafa

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引用次数: 0

摘要

在本文中，我们考虑粘弹性波动方程$$u_{tt}-\增量u+\int_0^{t}g（t-s）\Δu（s）ds+a|u_t|^｛m（\cdot）-2｝u_t=0$$，具有具有可变指数\（m（x）\）的非线性反馈。我们研究了两种类型阻尼之间的相互作用，并在松弛函数（g\）的一般假设下建立了最佳衰减结果。我们构造了显式公式，它提供了比文献中已有的更快的能量衰减率。有关更多信息，请参阅https://ejde.math.txstate.edu/Volumes/2023/53/abstr.html

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Optimal energy decay rates for viscoelastic wave equations with nonlinearity of variable exponent

In this article, we consider the viscoelastic wave equation $$ u_{tt}-\Delta u+\int_0^{t}g(t-s)\Delta u(s)ds+a| u_t| ^{m(\cdot )-2}u_t=0 $$ with a nonlinear feedback having a variable exponent $m(x)$. We investigate the interaction between the two types of damping and establish an optimal decay result under very general assumptions on the relaxation function $g$. We construct explicit formulae which provide faster energy decay rates than the ones already existing in the literature. For more information see https://ejde.math.txstate.edu/Volumes/2023/53/abstr.html

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