Introduction Of Research Advance For Discontinuous Solutions Of The Quasilinear Hyperbolic Equation

This paper is a comprehensive introduction to the research advance and some main results of the BV solution for one-order quasilinear hyperbolic equation with measure as initial condition and one-order quasilinear hyperbolic systems solutions in the recent ten years, which is generally composed of three parts.The first part mainly introduces the research advace of the BV solution for one-order quasilinear hyperbolic equation with measure as initial condition in the following.One-order Quasilinear Hyperbolic Equation:The second part mainly introduces the research advace of the solutions for one-order quasilinear hyperbolic systems in the following.One-order Quasilinear Hyperbolic Systems:where n＞1, u is an unknown vector function, u-{u1,u2,…, un)T, T says transposed, g is a vector function, g=(g1, g2,…, gn)T,and Ai (i= 1,…, k) is the known n×n-order matrix function.The third part briefly explains the some problems to be solved.