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This paper is concerned with entropy solutions of scalar conservation laws of the form ₓu+ f=0 in Rᵈ (0, ). The flux f=f (x, u) depends explicitly on the spatial variable x. Using an extension of Kruzkov's method, we establish the L¹-contraction property of entropy solutions under minimal regularity assumptions on the flux.
Paz Hashash (Thu,) studied this question.