论文标题
景观演化模型的适应性和稳定性分析
Well-posedness and stability analysis of a landscape evolution model
论文作者
论文摘要
在本文中，我们考虑了建模景观演变的部分微分方程系统。地面被沉积或稀释的水流动侵蚀。该系统由地面高度，流体高度和流体层中的沉积物浓度组成的三个进化方程组成。我们首先考虑系统的适合性，并表明它在短时间内被很好地摆姿势，并假设初始流体高度不会消失。然后，在薄膜流过倾斜的易生蚀面平面的情况下，我们将重点放在图案形成上。为此，我们对恒定状态解决方案进行光谱稳定性分析，以确定不稳定性条件并确定模式形成的机制。这些模式，即rill和鸥，是景观中河流和山谷形成的起点。最后，我们对完整系统进行了一些数值模拟，以验证光谱不稳定性方案并确定所得模式。
In this paper, we consider a system of partial differential equations modeling the evolution of a landscape. A ground surface is eroded by the flow of water over it, either by sedimentation or dilution. The system is composed by three evolution equations on the elevation of the ground surface, the fluid height and the concentration of sediment in the fluid layer. We first consider the well-posedness of the system and show that it is well posed for short time and under the assumption that the initial fluid height does not vanish. Then, we focus on pattern formation in the case of a film flow over an inclined erodible plane. For that purpose, we carry out a spectral stability analysis of constant state solutions in order to determine instability conditions and identify a mechanism for pattern formations. These patterns, which are rills and gullies, are the starting point of the formation of rivers and valleys in landscapes. Finally, we make some numerical simulations of the full system in order to validate the spectral instability scenario, and determine the resulting patterns.
