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In this paper, we present and apply a computer-assisted method to studysteady states of a triangular cross-diffusion system. Our approach consist inan a posteriori validation procedure, that is based on using a fxed pointargument around a numerically computed solution, in the spirit of theNewton-Kantorovich theorem. It allows us to prove the existence of various nonhomogeneous steady states for different parameter values. In some situations,we get as many as 13 coexisting steady states. We also apply the a posteriorivalidation procedure to study the linear stability of the obtained steadystates, proving that many of them are in fact unstable.

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