Global Boundedness of Solutions to a Quasilinear Chemotaxis System with Nonlocal Nonlinear Reaction

This work studies a class of chemotaxis systems generalizing the prototype {[ u_t= d∇· ( (1+u)^m-1∇ u) - χ∇· (u(1+u)^σ -2∇ v) +μ u^α ( 1-∫ _Ωu^β ),; 0= Δ v-v+ u, ]. with nonnegative initial data under zero-flux boundary conditions in a smooth bounded domain Ω⊂ℝ^N (N≥ 1) , where d , m , χ , μ >0 , σ≥ 1 , and α , β >1 . In this paper, it is rigorously proved that a global classical solution exists under the condition σ +N/2(σ -m)-β< α 更多