On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport

This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth. These are non-local variants of the corresponding local model proposed by H. Garcke et al. (2016), and take into account the long-range interactions occurring in biological phenomena. The model in consideration couples a nonlocal Cahn-Hilliard equation for the tumor phase variable with a reaction-diffusion equation for the...