Comparison principle for Walsh's spider HJB equations with non linear local time Kirchhoff's boundary transmission
Analysis of PDEs
2025-01-31 v2
Abstract
The main purpose of this work is to obtain a comparison principle for viscosity solutions of a system of elliptic Walsh's spider Hamilton-Jacobi-Bellman equations, possessing a new boundary condition called non linear local-time Kirchhoff's transmission. The main idea is to build test functions at the neighborhood of the vertex solutions of ODE, with well-designed coefficients. The key point is to impose a 'local-time' derivative at the vertex absorbing the error term induced by - what we decide to call here - the Kirchhoff's speed of the Hamiltonians.
Keywords
Cite
@article{arxiv.2312.01362,
title = {Comparison principle for Walsh's spider HJB equations with non linear local time Kirchhoff's boundary transmission},
author = {Isaac Ohavi},
journal= {arXiv preprint arXiv:2312.01362},
year = {2025}
}