Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems

Abstract: The continuous dependence on the initial data and consequently the uniqueness of bounded weak solutions to a class of triangular reaction-cross-diffusion equations is shown. The class includes doubly degenerate equations for nutrient taxis models describing the response of bacteria to nutrient conditions. The proof is based on a careful use of the $H^{-1}$ method. The present manuscript is in draft form and will be revised soon.