Global boundedness in a quasilinear chemotaxis model with nonlinear diffusion and consumption of chemoattractant

Abstract

This paper proves the global existence and boundedness of solutions to a quasilinear chemotaxis model with nonlinear diffusion and consumption of chemoattractant defined on a smooth bounded domain with no‐flux boundary conditions under some assumptions. The result holds for arbitrary nonnegative sensitivity coefficients and domains in the spatial dimension which is no less than two.