2022/02/05 by Hitoshi Ishii, Ishii, Hitoshi
Computer Science · Mathematics · #35B40 #35D40 #35F50 #49L25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2202.02507
openalex publication_date 2022/02/05 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In recent years there has been intense interest in the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto has recently given an example of the Hamilton-Jacobi equation having non-convex Hamiltonian in the gradient variable, for which the full convergence of the solutions does not hold as the discount factor tends to zero. We give here an explicit example of nonlinear monotone systems of Hamilton-Jacobi equations having convex Hamiltonians in the gradient variable, for which the full convergence of the solutions fails as the discount factor goes to zero.