Abstract
We prove here that limits of nonnegative solutions to reaction-diffusion systems whose nonlinearities are bounded in L 1 always converge to supersolutions of the system. The motivation comes from the question of global existence in time of solutions for the wide class of systems preserving positivity and for which the total mass of the solution is uniformly bounded. We prove that, for a large subclass of these systems, weak solutions exist globally.Mathematics Subject Classification (2000)35K1035K4535K57Key wordsparabolic systemreaction-diffusionblowupglobal existencesemilinear system
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