Cauchy Problem For Quasilinear Hyperbolic Systems

Cauchy Problem for Quasilinear Hyperbolic Systems

Cauchy Problem for Quasilinear Hyperbolic Systems

This book is concerned with Cauchy problem for quasilinear hyperbolic systems. By introducing the concepts weak linear degeneracy and matching condition, we give a systematic presentation on the global existence, the large time behaviour and the blow-up phenomenon, particularly, the life span of C 1 solutions to the Cauchy problem with small and decaying initial data. Some successful applications of our general theory are given to the quasilinear canonical system related to the Monge-Ampére equation, the system of nonlinear three-wave interaction in plasma physics, the nonlinear wave equation with higher order dissipation, the system of one-dimensional gas dynamics with nonlinear dissipation, the system of motion of an elastic string, the system of plane elastic waves for hyperelastic materials and so on.

On the Cauchy Problem for Quasilinear Hyperbolic Systems of Partial Differential-functional Equations of the First Order