Blow‐Up Curve for a Quasilinear Two‐Species Chemotaxis System With Two Chemicals in Higher Dimension

ABSTRACT In this article, two‐species chemotaxis model with nonlinear diffusion function and chemotactic sensitivity function satisfying for all has been considered in a bounded domain , , where and are such that with for all , . Global existence and boundedness of solutions were shown if . Moreover, we could construct initial data such that the corresponding solution must be unbounded provided that , which actually gives a critical curve for the quasilinear problem in higher dimension.