Global well-posedness of a quasilinear chemotaxis-haptotaxis system with indirect signal production

In this paper, we consider a quasilinear chemotaxis-haptotaxis model with indirect signal production, subject to Neumann boundary conditions. Under some suitable assumptions on the parameters χ and μ, it is shown that, in n≥1, either strong diffusion or strong logistic damping guarantees global existence of bounded classical solutions for all suitably regular initial data. Moreover, we can establish exponential decay of w.