Global solvability and boundedness to a attraction-repulsion model with logistic source

In this paper, we deal with an attraction-repulsion model with a logistic source as follows: { u(t)=Delta u-chi del<middle dot>(u del v)+xi del<middle dot>(u del w)+mu u(q)(1 -u) in Q, v(t)=Delta v-alpha(1)v+beta(1)u in Q w(t)=Delta w-alpha(2)w+beta(2)u in Q where Q=Omega xR+,Omega subset of R-3 is a bounded domain. We mainly focus on the influence of logistic damping on the global solvability of this model. In dimension 2,qcan be equal to 1 (Math. Methods Appl. Sci. 39(2):289-301,2016). In dimension 3, we derive that the problem admits a global bounded solution when q>8/7. In fact, we transfer the difficulty of estimation to the logistic term through iterative methods, thus,compared to the results in (J. Math. Anal. Appl. 2:4482017;Z.Angew.Math.Phys.73(2):1-252022) in dimension 3, our results do not require any restrictions on the coefficients.