2023/04/26 by Shimpei Makida, Makida, Shimpei · 1 citation
Computer Science · #35D40 #35R02 #49L25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2304.13544
openalex publication_date 2023/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove the stability of viscosity solutions of the Hamilton--Jacobi equations for a sequence of networks embedded in Euclidean space. The network considered in this paper is not merely a graph -- it comprises a collection of line segments. We investigate the conditions under which the stability of viscosity solutions holds if the sequence of networks converges to some compact set in the Hausdorff sense. As a corollary, a characterization of the limit of a sequence of networks on which viscosity solutions can be considered, is obtained. In consideration of this problem, we adopt the concept of viscosity solutions as presented in the sense of Gangbo and Święch.