Behavior in time of solutions to a degenerate chemotaxis system with flux limitation

We study a new class of Keller-Segel models, which presents a limited flux and an optimal transport of cells density according to chemical signal density. As a prototype of this class we study radially symmetric solutions to the parabolic-elliptic system { = del center dot(del/root(2)+|del|(2)) -del center dot(del(1+|del|(2))), is an element of, >0, 0 =-+, is an element of, >0 under no flux boundary conditions in a ball = subset of and initial condition(,0) =(0)()>0, >0, >0, >0 and =1/|| integral(0).Under suitable conditions onand0it is shownthat the solution blows up in infinity-norm at a finite time and for some >1it blows up also in-norm. The proofs are mainly based on an helpful change of variables, on comparison arguments and some suitable estimates.