Estimation Of The Maximal Existence Time Of Classical Solutions To Partially Dissipative Quasilinear Hyperbolic Systems

In this paper, we consider partial dissipative frst-order quasilinear hyper-bolic systems with a characteristic feld which is neither strictly dissipative norweakly linearly degenerated. We investigate the problem of the global existenceof classical solutions. A series of weighted semi-norms are defned and estimated.By using a bootstrap argument, a lower bound of the blow-up time is obtained.By the comparison principle of ordinary diferential equations, we also get anupper bound of the blow-up time. Thus, the classical solutions will blow up infnite time. An estimate of the blow-up time is obtained.