TY - JOUR
T1 - Life-span of Classical Solutions of Initial-boundary Value Problem for First Order Quasilinear Hyperbolic Systems
JO - Journal of Partial Differential Equations
VL - 2
SP - 131
EP - 154
PY - 2007
DA - 2007/05
SN - 20
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5298.html
KW - Quasilinear hyperbolic system
KW - mixed initial-boundary value problem
KW - life-span
KW - weak linear degeneracy
AB - <p>In this paper, we consider the mixed initial-boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in a half-unbounded domain {(t, x)|t ≥ 0, x ≥ 0}. Under the assumption that the positive eigenvalues are not all weakly linearly degenerate, we obtain the blow-up phenomenon of the first order derivatives of C¹ solution with small and decaying initial data. We also give precise estimate of the life-span of C¹ solution.</p>