Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give the explicit decay rates for the energy, but do not address reflection/transmission of waves at the interface of the damping. Still for a subset of the models considered, this represents the first result proving the decay of the energy of the surface wave models.

翻译：受无黏欧拉方程表面波数值建模的启发，我们分析了阻尼水波的线性模型，并建立了具有足够光滑初始构型的能量衰减性质。研究结果给出了能量的显式衰减率，但未涉及阻尼界面处波的反射/透射问题。尽管如此，对于所考虑的模型子集而言，这是首次证明表面波模型能量衰减的结果。