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The purpose of this paper is to prove global existence of solutions forgeneral systems of reaction diffusion equations with nonlinearities for whichonly two main proprieties hold: Quasi-Positivity and balance law but with twodifficulties: they change sign and with unlimited polynomial growth. Weovercome the first difficulty by fixing the reaction sign after some time andthe second one by using a judicious polynomial Lyapunov functional.

Global existence for reaction diffusion systems with strict balance Law and nonlinearities with non constant-sign and unlimited polynomial growth