A uniqueness result for a semilinear parabolic system

We prove that for nonnegative, continuous, bounded and nonzero initial data we have a unique solution of the reaction–diffusion system described by three differential equations with non-Lipschitz nonlinearity. We also find the set of all nonnegative solutions of the system when the initial data is zero and in the last section we briefly discuss a generalization of the theorem to a system of n equations.