Investigating the Continuum Limit of a Follow-The-Leader Model with Inhomogeneous Road Conditions
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An investigation of the continuum limit of Follow-the-Leader model with inhomogeneous road conditions and its relation to the LWR model. In the special case when the flux function have one discontinuity that decreases the existence of a continuum limit, for a subsequence, is proven. This is done using techniques from analysis of numerical schemes for conservation laws with discontinuous flux. Especially compensated compactness play an impotent role in the proof. The limit is then shown to also satisfy the weak solution of the LWR model. Lastly there are presented some evidence indicating that the limit could also satisfy the entropy conditions with a discussion of the consequences if the entropy conditions is satisfied.