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

We derive the global existence of weak solutions of the Shigesada-Kawasaki-Teramoto systems in any space dimension d≥1 with a rather general condition on the coefficients. The existence is established using finite differences in time with truncations and an argument of Stampacchia's maximum principle to show the positivity of the solutions. We derive also the existence of a weak global attractor.