We consider the periodic initial-value problem for the Serre equations of water-wave theory and its semidiscrete approximation in the space of smooth periodic polynomial splines. We prove that the semidiscrete problem is well posed, locally in time, and satisfies a discrete positivity property for the water depth.

翻译：我们考虑的是水波理论Serre方程式的周期初始价值问题及其在平滑周期多球样条空间的半分位近似值问题。 我们证明半分位问题在当地及时提出并满足了水深的离散现实特性。