Global boundedness of weak solutions to a chemotaxis–haptotaxis model with p-Laplacian diffusion.

In this paper we study a chemotaxis–haptotaxis model with p-Laplacian diffusion and non-flux boundary condition u t = ∇ · (| ∇ u | p - 2 ∇ u) - χ ∇ · (u ∇ v) - ξ ∇ · (u ∇ w) + μ u (1 - u - w) , (x , t) ∈ Ω × (0 , T) , v t = Δ v - v + u , (x , t) ∈ Ω × (0 , T) , w t = - v w , (x , t) ∈ Ω × (0 , T) , where Ω ⊂ R n (n ≥ 1) is a bounded domain with smooth boundary ∂ Ω . We prove that when the diffusion parameter is appropriately large, i.e., p larger than some certain value, the global boundedness of the solutions does not depend on the relationship between the coefficient of logistic source term μ and the coefficient of chemotaxis term χ . And we find that the haptotaxis term does not affect the global boundedness of the solutions, in the other words, our result is consistent with the conclusion with no haptotaxis term (Zhuang et al. in Z Angew Math Phys 72:161, 2021). [ABSTRACT FROM AUTHOR]