Life-span of Classical Solutions of Initial-boundary Value Problem for First Order Quasilinear Hyperbolic Systems

Abstract

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.