Abstract:We consider the following quasilinear attraction-repulsion chemotaxis system of parabolic-elliptic-elliptic type with logistic source under homegeneous Neumann boundary conditions in a bounded domain `\Omega\subset R^{n}(n\geq2)` with smooth boundary, where`D(u)\geq c_{D}(u+1)^{m-1}` with `m\geq1`and `c_{D}>0`, `f(u)\leq a-bu^{\eta}` with `\eta>1`.{ We show two cases that the system admits a uniqueglobal bounded classical solution depending on `0\leq S(u)\leq C_{s}(u+1)^{q}, 0\leq F(u)\leq C_{F}(u+1)^{g}… Show more
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