Weak solutions and supersolutions in \(L^1\) for reaction-diffusion systems (Q1565973)

The author proves that limits of nonnegative solutions to reaction-diffusion systems, whose nonlinearities are bounded in \(L^1\), always converge to supersolutions of the system. The paper is motivated by the general 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.