A locally quadratic Glimm functional and sharp convergence rate of the Glimm scheme for nonlinear hyperbolic systems

F. Ancona, A. Marson

Consider the Cauchy problem for a strictly hyperbolic, $N\times N$ quasilinear system in one space dimension $$ u_t+A(u) u_x=0,\qquad u(0,x)=\bar u(x), \eqno (1) $$ where $u \mapst…