Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof (Q1704549)

The authors develop a computer-assisted method to study steady states of a triangular cross-diffusion system. The approach relies on an a posteriori validation procedure being based on a fixed point argument around the numerically computed solution in the spirit of the Newton-Kantorovich theorem. Such an approach allows to establish the existence of various non-homogeneous steady states for different parameter values. The a posteriori validation procedure is also employed to study the linear stability of the obtained steady states, proving that many of them are in fact unstable.