Classical solvability of nonlinear initial-boundary problems for   first-order hyperbolic systems
  We prove the global classical solvability of initial-boundary problems for semilinear first-order hyperbolic systems subjected to local and nonlocal nonlinear boundary conditions. We also establish lower bounds for the order of nonlinearity demarkating a frontier between regular cases (classical solvability) and singular cases (blow-up of solutions). 
Irina Kmit