A quasilinear chemotaxis–haptotaxis model: The roles of nonlinear diffusion and logistic source

In this paper, we study the following quasilinear chemotaxis–haptotaxis system [formula presented] in a bounded smooth domain Ω ⊂ ℝⁿ (n ≥ 1) under zero-flux boundary conditions, where the nonlinearities D, S₁, and S₂ are supposed to generalize the prototypes[formula presented] with r > 0 and b > 0. If the nonnegative initial data u₀(x) ϵ W^{1, ∞} (Ω),v₀ (x) ϵ W^{1, ∞} (Ω), and w₀(x) ϵ C^{2 α} (Ω). for some [formula presernted] then (*) has a unique nonnegative classical solution, which is globally bounded. [formula presernted] then (*) has a unique nonnegative classical solution, which is globally bounded. [formula presernted] then (*) has a unique nonnegative classical solution, which is globally bounded.