Local and global solvability in attraction-repulsion chemotaxis systems with L2-initial data
Keywords:
abstract evolution equations, $L^2$-initial data, local existence, attraction-repulsion chemotaxis systemsAbstract
This paper deals with the attraction-repulsion chemotaxis system under homogeneous Neumann initial-boundary conditions, where Ω ⊂ Rn (n ≤ 3) is a smoothly bounded domain and a,b,c,χ,ξ,α,β,γ,δ > 0 and τ ∈ {0, 1} are constants. The purpose of the present paper is to construct a local solution of this system for any L2-initial data without additional conditions on χ and ξ by using the theory for abstract evolution equations and to extend the local solution globally in the repulsion-dominant case by relying on a priori estimates.
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