Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics (Journal of Partial Differential Equations, 2003)
" 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."
Keywords: Initial-boundary value problem; global C¹ solution; quasilinear hyperbolic system of diagonal form; linearly degenerate characteristics