Degenerate Cahn–Hilliard and incompressible limit of a Keller–Segel model

The Keller-Segel model is a well-known system representing chemotaxis in living organisms. We study the convergence of generalized nonlinear variant to degenerate Cahn-Hilliard system. This analysis made possible from observation that equivalent relaxed version Furthermore, this latter has an interesting application modelling tissues. Indeed, compressible and incompressible porous medium type equations are widely used describe mechanical properties system, can be viewed as tissue for which movement driven by Darcy's law takes into account effects viscosity well surface tension at tissue. equation some analytical such limit our model. Our relies on priori estimates, compactness properties, equivalence between