A note on blow-up phenomenon of classical solutions to quasilinear hyperbolic systems (Q1599969)

This paper deals with the following quasilinear system: \[ {\partial u\over\partial t}+A(u){\partial u\over\partial x}=0, \tag{1} \] where \(u=(u_1,\dots,u_n)^T\) is the unknown vector function of \((t,x)\) and \(A(u)= (a_{ij} (u))\) is an \((n\times n)\) matrix with elements \(a_{ij}(u)\), \(i,j=1, \dots,n\). Assuming some smoothness on \(a_{ij}\) and strict hyperbolicity of (1) in a neighbourhood of \(u=0\), the authors study blow-up phenomena of classical solutions to quaslinear hyperbolic systems (1).