We study the limiting behaviour of the Cauchy problem for a class of Carleman-like models in the diffusive scaling with data in the spaces Lp, 1≤p≤∞. We show that, in the limit, the solution of such models converges towards the solution of a nonlinear diffusion equation with initial values determined by the data of the hyperbolic system. When the data belong to L1, a condition of conservation of mass is needed to uniquely identify the solution in some cases, whereas the solution may disappear in the limit in other cases
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