论文标题
自然边界条件下雷诺方程的存在和独特性
Existence and Uniqueness of Reynolds equation under natural boundary conditions
论文作者
论文摘要
对于在自然边界条件下求解雷诺方程的问题，可以通过假设自由边界获得相应的假设解决方案。如果解决方案满足自然边界条件，则边界是我们正在寻找的边界。显然，所有的边界都形成了一个集合，假定解决方案为正。我们证明了S的最大元素与自然状况之间的等效性。我们证明了添加的集合的亲密关系。因此，我们证明该集合必须具有独特的最大元素。此外，我们在自然边界条件下获得了雷诺方程解决方案的独特性和存在。 在工程中，零设置方法通常用于找到雷诺方程的边界，我们还提供了证明零设置方法仅具有一个迭代错误解决方案。我们给出了一种在一维条件下求解雷诺方程的算法，该方程达到了理论上的上限。 最后，我们讨论了该方法的物理含义。
For the problem of solving Reynolds equation under natural boundary conditions, the corresponding hypothetical solution can be obtained by assuming the free boundary. If the solution satisfies natural boundary conditions, then the boundary is the boundary we are looking for. Obviously, there is a set S formed by all the boundaries that assume the solution is positive. We prove equivalence between maximum element of S and natural condition. We prove the closeness of set S under addition. Therefore, we prove that the set S must have a unique greatest element. Furthermore, we obtain the uniqueness and existence of solutions of Reynolds equation under natural boundary conditions. In engineering, the zero setting method is often used to find the boundary of Reynolds equation, and we also give the proof that the zero setting method has only one iterative error solution. We give an algorithm for solving Reynolds equation under one-dimensional conditions, which reaches the theoretical upper bound. We discuss the physical meaning of this method at the end.
