Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems (Journal of Partial Differential Equations, 2002)
In this paper, we consider Cauchy problem for general first order inho- mogeneous quasilinear strictly hyperbolic systems. Under the matching condition, we first give an estimate on inhomogeneous terms. By this estimate, we obtain the asymptotic behaviour for the life-span of C¹ solutions with “slowly” decaying and small initial data and prove that the formation of singularity is due to the envelope of characteristics of the same family.
Keywords: Quasilinear hyperbolic system; matching condition; life-span; weak linear degeneracy