We study a semi-linear initial-value problem arising from a Boltzmam like model of vahicular traffic an a motor way supposed infinite and without entrances and exits.We prove the existence and uniqueness of the local (in Time) "mild" solution u(t) in L^1 and its positivity, if the initial condition u<sub>_c</sub> = u(0) is positive and belougs to L^1 \cap L^∈fty. Finally,we consider the "mollified" version of the problem,already in another paper,and we show that unique strit solution u_{ε}(t) is such that lim_{ε → 0<sup>+</sup>} \big\Vert u_epsilon(t) - u(t) \big\Vert = 0 uniformly in t ∈ [0, \buildrel \_ \over t] with  \buildrel \_ \over t suitably chosen.

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