A necessary and sufficient condition for global existence of classical solutions to Cauchy problem of quasilinear hyperbolic systems in diagonal form. (English) Zbl 0968.35073
Summary: This article considers the Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition guaranteeing the existence of a unique global classical solution on \(t\geq 0\) is obtained, and a sharp estimate of the life span for the classical solution is given.
MSC:
35L60 | First-order nonlinear hyperbolic equations |
35B40 | Asymptotic behavior of solutions to PDEs |
35L45 | Initial value problems for first-order hyperbolic systems |
35L65 | Hyperbolic conservation laws |