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 = Δu—X▽·(u▽w)，0 =Δv—αv + βw、,wt = Δw-ζ▽—·(w▽z),0 = Az—γz + δu inΩ x(0,T),where smooth bounded domainΩ(?)RN(N ≥ 2),the coefficientsα,β,γ,δ 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∫Ω(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.