Two Types Of Overall Existence Of Staggered Diffusion Equations With Chemotaxis

We investigate a biological model for chemotaxis as follows:We study the global existence in different cases for the above system.The global existence of the solution is always the difficult problem of the chemotaxis model.On the first half, we prove the global existence of the solution with semigroup theory ,Moser iteration,interpolation inequalities.We expand f(u)=u,χ(v) = v which is in the results of Hillen and Potapov([17]) to i(u)=u,χ(v) = (1 + v)^1+βandβis a bounded const.On the second half,we consider a special biological model and we prove the global existence of the solution of that model.