Strong ergodic properties of a first-order partial differential equation (Q1120721)

Consider the initial value problem of the first order nonlinear PDE \[ (1)\quad u_ t+C(x)u_ x=f(x,u),\quad (x,t)\in [0,\infty)\times [0,1],\quad u(0,x)=v(x),\quad x\in [0,1]. \] Under some conditions, (1) generates a semiflow \(\{S_ t\}_{t\geq 0}\) on C[0,1] defined by \(S_ tv(x)=u(t,x)\), where u is the solution of (1). This paper shows one existence of an exact invariant measure \(\mu\) having some additional properties. From that follow additional features of \(\{S_ t\}:\) chaos and the existence of turbulent trajectories.