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This paper is devoted to the grazing collision limit of the inelastic Kac model introduced in [PT04], when the equilibrium distribution function is a heavy-tailed Lévy-type distribution with infinite variance. We prove that solutions in an appropriate domain of attraction of the equilibrium distribution converge to solutions of a Fokker-Planck equation with(More)
∂tu = ∆u + f(u) u(0) = u0 where u(t, x) : R × R → R, and f ∈ C(R,R) is a given function with f(0) = 0. It is well-known that if the initial data u0 belong to L ∞(Rn) then there exist T (u0) > 0 and a unique solution u ∈ C ([0, T [,L ∞(Rn)). In this paper we will consider initial data u0 which do not belong to L ∞(Rn). At first we will review the known(More)
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