Author:
Eckardt Maria,Surulescu Christina
Abstract
AbstractStarting from a mesoscopic description of cell migration and intraspecific interactions, we obtain by upscaling an effective reaction–diffusion–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.
Funder
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
Publisher
Springer Science and Business Media LLC
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