Abstract: In this paper we prove a general existence result for bounded weak solutions of the following class of hyperbolic systems of conservation laws in several space dimensions
∂t ui + ∑α=1:n ∂xα (fα(|u|) ui) = 0, ui(0,⋅) = vi(&sdot)where f∈W1,∞loc and v∈L∞ with |v|≥c>0 $\leb^n$-a.e and |v|∈BVloc
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