Global Existence for Coupled Reaction Diffusion Systems

We prove here global existence in time of classical solutions for reaction diffusion systems with strong coupling in the diffusion and with natural structure conditions on the nonlinear reactive terms. This extends some similar results in the case of a diagonal diffusion-operator associated with nonlinearities preserving the positivity and the total mass of the solutions or for which the total mass is a priori bounded. Here, however, no positivity assumption is made since nondiagonal systems do not preserve it.