论文标题
在包含给定数据的顶点的HyperGraph上的热方程
Heat equation on the hypergraph containing vertices with given data
论文作者
论文摘要
本文涉及由HyperGraph Laplacian控制的多相多的普通微分方程的库奇问题，该方程描述了``热''或``'heat''或``粒子''在超盖的顶点上的扩散。我们认为，观察者内部对几个顶点上的热量进行操作，即通过某些给定功能固定。这种情况可以简化为与时间依赖性的亚分体操作员相关的非线性进化方程，该操作员在以前的许多研究中都研究了其可溶性。但是，在本文中，我们给出了可溶性的替代证明，以避免因时间依赖性亚不同的链条规则引起的一些复杂的计算。至于已知的抽象理论无法确保的结果，我们还讨论了解决方案对给定数据的连续依赖性以及解决方案的时间全球行为。
This paper is concerned with the Cauchy problem of a multivalued ordinary differential equation governed by the hypergraph Laplacian, which describes the diffusion of ``heat'' or ``particles'' on the vertices of hypergraph. We consider the case where the heat on several vertices are manipulated internally by the observer, namely, are fixed by some given functions. This situation can be reduced to a nonlinear evolution equation associated with a time-dependent subdifferential operator, whose solvability has been investigated in numerous previous researches. In this paper, however, we give an alternative proof of the solvability in order to avoid some complicated calculations arising from the chain rule for the time-dependent subdifferential. As for results which cannot be assured by the known abstract theory, we also discuss the continuous dependence of solution on the given data and the time-global behavior of solution.
