Abstract
This paper deals with the Cauchy problem for a quasilinear first-order equation that includes a possibly discontinuous hysteresis operator F : ∂ ∂ t [ u + F ( u ) ] + ∂ u ∂ x = f in R , for t > 0 . Existence of a weak solution is proved for F equal to a completed relay operator. In the case of f ≡ 0 , an entropy-type condition yields Lipschitz-continuous and monotone dependence on the initial data, hence uniqueness.
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