This paper is concerned with entropy solutions of scalar conservation laws of the form ∂ₜu+ 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.
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Paz Hashash (2024) studied this question.