Long-time effect of relaxation for hyperbolic conservation laws
The author deals with a strictly hyperbolic system of conservation laws with relaxation of the form \[ u_t+ f(u, v)_x= 0,\quad v_t+ g(u, v)_x= h(u, v). \] Such equations appear in many physical systems. It is shown that the long-time effect of relaxation is equivalent to a viscous effect when the initial data is a perturbation of a constant equilibrium state. The corresponding solution tends to a diffusion wave time asymptotically. This diffusion wave carriers an invariant mass. The convergence rate to this diffusion in \(L^p\)-sense \((1\leq p\leq \infty)\) is also obtained and this rate is optimal.
scientific article; zbMATH DE number 878030