This paper considers the Cauchy problem for hyperbolic conservation laws arising in chromatography:
with bounded measurable initial data, where the relaxation term g(δ, u, v) converges to zero as the parameter δ > 0 tends to zero. We show that a solution of the equilibrium equation
is given by the limit of the solutions of the viscous approximation
of the original system as the dissipation ε and the relaxation δ go to zero related by δ = O(ε). The proof of convergence is obtained by a simplified method of compensated compactness , avoiding Young measures by using the weak continuity theorem (3.3) of two by two determinants.
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