Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics

Abstract

" We prove that the C\u00ba boundedness of solution implies the global existence and uniqueness of C\u00b9 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C\u00b9 solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity."