BOUNDEDNESS IN AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH BOTH NONLINEAR SIGNAL PRODUCTION AND CONSUMPTION

This paper is concerned with the following homogeneous Neumann initial-boundary value problem for a chemotaxis system { ut= triangle u-chi del<middle dot>(u del v) +xi del<middle dot>(u del w), x is an element of ohm, t >0, vt= triangle v-v+v gamma 11,0 = triangle v1-v1+u gamma 2, x is an element of ohm, t >0, wt= triangle w-u gamma 3w, x is an element of ohm, t >0, in a smooth bounded domain Omega C R- n ( n > 2) , where the parameters satisfy chi, xi, gamma 1 , gamma 2 , gamma 3 > 0 . It has been shown that if gamma (1) gamma( 2) < 2/ n and gamma (3) < 2/ n+2 , then the system possesses a global classical solution. In this work, we improve some previous results.