Global weak solutions to a doubly haptotactic cross-diffusion system with \(p\)-Laplacian diffusion (Q6595506)

This paper considered a doubly haptotactic cross-diffusion system with \(p\)-Laplacian diffusion. Under Neumann boundary conditions in a bounded domain \(\Omega\subset R^{2}\) 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.\N\NThe proof of the main results utilizes various tools from prior literature on simpler systems, but it also contains several original ideas that have been meticulously developed, particularly in the arguments presented in Section 3--Section 7. Moreover, the analysis is generally robust.