具有摩擦和粘弹性阻尼项的非线性wave equations方程整体解的大时间收敛性
Large time behaivor of global solutions to nonlinear wave equations with frictional and viscoelastic damping terms
摘要：
本文研究了一类具有摩擦阻尼项和粘弹性阻尼项的非线性波动方程的Cauchy问题。正如文献[8]所指出的，在这种组合中，对于线性方程的全局动力学，摩擦阻尼项对于粘弹性阻尼项是占主导地位的。在本说明中，我们观察到，如果初始数据较小，即使在非线性方程的情况下，摩擦阻尼项也会再次占主导地位。换句话说，我们的主要结果是扩散现象：解决方案是近似的热核与适当的常数。我们的证明是基于相应的线性方程的几个估计。
英文摘要：
In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. As is pointed out by [8], in this combination, the frictional damping term is dominant for the viscoelastic one for the global dynamics of the linear equation. In this note we observe that if the initial data is small, the frictional damping term is again dominant even in the nonlinear equation case. In other words, our main result is diffusion phenomena: the solution is approximated by the heat kernel with a suitable constant. Our proof is based on several estimates for the corresponding linear equations.
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