We study the nonlinear damped wave equation with a linear pumping and a convective nonlinearity. We consider the solutions, which satisfy the periodic boundary conditions. Our aim is to prove global existence of solutions to the periodic problem for the nonlinear damped wave equation by applying the energy‐type estimates and estimates for the Green operator. Moreover, we study the asymptotic profile of global solutions.

中文翻译：

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对流非线性非线性阻尼波方程的周期问题

我们研究了具有线性泵浦和对流非线性的非线性阻尼波方程。我们考虑满足周期边界条件的解。我们的目的是通过应用Green-operator的能量类型估计和估计来证明非线性阻尼波方程的周期问题的解的全局存在。此外，我们研究了整体解的渐近曲线。