  Starting from a mesoscopic description of cell migration and intraspecific
interactions we obtain by upscaling an effective reaction-difusion-taxis
equation for the cell population density involving spatial nonlocalities in the
source term and biasing its motility and growth behavior according to
environmental acidity. We prove global existence, uniqueness, and boundedness
of a nonnegative solution to a simplified version of the coupled system
describing cell and acidity dynamics. A 1D study of pattern formation is
performed. Numerical simulations illustrate the qualitative behavior of
solutions.
