Bruno Volzone

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Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model [10]. The implications of nonlinear diffusion are that solutions exist globally and are uniformly bounded in time. We analyse the stationary case showing the existence of a unique, up to(More)
(1) ∂tρ = ∆ρ m +∇ · (ρ∇(W ∗ ρ)), essendo W ∈ C(R \ {0}), d ≥ 2 un opportuno nucleo di aggregazione, nell’ipotesi in cui la diffusione degenere sia dominante, ossia m > 2 − 2/d. In particolare, se nel caso bidimensionale si assume che W sia il classico nucleo di aggregazione logaritmico, si mostrerà che esiste un unico stato stazionario del modello (1) e che(More)
Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to the quadratic singularity without violating the inequality, and even a whole asymptotic expansion can be build, with(More)
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