Study On A Keller-Segel Chemotaxis Model With Two-species

The paper considers the following two-species chemotaxis system with two chem?icals with homogeneous Neumann boundary conditions:ut = ?u—X?·(u?w)?0 =?v—?v + ?w?,wt = ?w-??—·(w?z),0 = Az—?z + ?u in? x(0,T),where smooth bounded domain?(?)RN(N ? 2),the coefficients?,?,?,? are non-negative.Concerning the finite time blow up of solutions to the system in radically symmetric situations and small initial data problem,it is proved when initial data??(u0(X)+w0(x))|x|N is small enough,the finite time blow up of solutions to the sys-tem in radically symmetric situations;if ||u0||Lr,||w0||Lr sufficiently small with r>N,there exists a unique global bound solution.