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We derive the global existence of weak solutions of theShigesada-Kawasaki-Teramoto systems in space dimension less or equal to 4 witha rather general condition on the coefficients. The existence is establishedusing finite differences in time with truncations and an argument ofStampachia's maximum principle to show the positivity of the solutions. Wederive also the existence of a weak global attractor.

Weak solutions of the Shigesaka-Kawasaki-Teramoto equations and their attractors