The Zero Relaxation Limit for 2x2 Hyperbolic Systems

In this paper we are concerned with the study of the relaxation of the following system of balance laws: ut + f(u; v)x = 0; vt + g(u; v)x = 1 ((u) − v); (1) with u0(x), v0(x) ∈ L∞ and f, g and smooth functions (for instance, f, g and ∈ C5). We assume that the system is strictly hyperbolic, namely −(u; v) ¡ +(u; v); where −(u; v), +(u; v) are the two characteristic speeds of Eq. (1). We want to prove the convergence of the weak solutions of Eq. (1) toward the solutions of the scalar conservation law ut + f(u; (u))x = 0