TY - JOUR
T1 - Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics
JO - Journal of Partial Differential Equations
VL - 1
SP - 8
EP - 17
PY - 2003
DA - 2003/02
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5401.html
KW - Initial-boundary value problem
KW - global C¹ solution
KW - quasilinear hyperbolic system of diagonal form
KW - linearly degenerate characteristics
AB -  We prove that the Cº boundedness of solution implies the global existence and uniqueness of C¹ solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C¹ 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.