Global weak solutions to a doubly haptotactic cross-diffusion system with $ p $-Laplacian diffusion

This paper investigates a doubly haptotactic cross-diffusion system with p-Laplacian diffusion.Under Neumann boundary conditions in a bounded domain Ω ⊂ R 2 with smooth boundary, it is proved that if p > 2 for all sufficiently smooth initial data, the model possesses at least one global weak solution.