On global existence of localized solutions of some nonlinear lattices
  We prove global existence and uniqueness of solutions of some important nonlinear lattices which include the Fermi-Pasta-Ulam (FPU) lattice. Our result shows (on a particular example) that the FPU lattice with high nonlinearity and its continuum limit display drastically different behaviour with respect to blow up phenomenon. 
G. Perla Menzala (National Laboratory of Scientific Computation,   Brasil) and V. V. Konotop (University of Lisbon, Portugal)