2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69670We construct an example of blow-up in a flow of min-plus linear operators arising as solution operators for a Hamilton-Jacobi equation with a Hamiltonian of the form |p|^alpha+U(x,t), where alpha>1 and the potential U(x,t) is uniformly bounded together with its gradient. The construction is based on the fact that, for a suitable potential defined on a time interval of length T, the absolute value of velocity for a Lagrangian minimizer can be as large as O((log T)^(2-2/alpha)). We also show that this growth estimate cannot be surpassed. Implications of this example for existence of global generalized solutions to randomly forced Hamilton-Jacobi or Burgers equations are discussed.19 pages, no figures; based on a talk given at the workshop "Idempotent Mathematics and Mathematical Physics" at the E. Schroedinger Institute for Mathematical Physics in Vienna in February 2003. A dedication indicating the untimely death of Dmitry Khmelev is addedOptimization and ControlDynamical Systems35L67; 49L99text