A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications
Analysis of PDEs
2023-03-09 v1 Optimization and Control
Abstract
We study continuous dependence estimates for viscous Hamilton- Jacobi equations defined on a network Gamma. Given two Hamilton-Jacobi equations, we prove an estimate of the C2-norm of the difference between the corresponding solutions in terms of the distance among the coefficients. We also provide two applications of the previous estimate: the first one is an existence and uniqueness result for a quasi-stationary Mean Field Games defined on the network Gamma; the second one is an estimate of the rate of convergence for homogenization of Hamilton-Jacobi equations defined on a periodic network, when the size of the cells vanishes and the limit problem is defined in the whole Euclidean space.
Keywords
Cite
@article{arxiv.2303.04629,
title = {A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications},
author = {Fabio Camilli and Claudio Marchi},
journal= {arXiv preprint arXiv:2303.04629},
year = {2023}
}