On a cross-diffusion population model deduced from mutation and splitting of a single species

We deduce a particular case of the population cross-diffusion model introduced by Shigesada et al. (1979) [1] by using the ideas of mutation and splitting from a single species, as described by Sánchez-Palencia for ODE’s systems Sánchez-Palencia (2011) [21]. The resulting equations of the PDE system only differ in the cross-diffusion terms, the corresponding diffusion matrix being self-diffusion dominated, which implies that the well known population segregation patterns of the Shigesada et al. model do not appear in this case. We prove existence and uniqueness of solutions of the PDE system and use a finite element approximation to discuss, numerically, stability properties of solutions with respect to the parameters in comparison with related models.