On the Blow-up of Solutions to Some Semilinear and Quasilinear Reaction-diusion Systems

Abstract. After a brief discussion of known global well-posedness results for semilinear systems, we introduce a class of quasilinear systems and obtain spatially local estimates which allow us to prove that if one component of the system blows up in nite time at a point x in space then at least one other component must also blow up at the same point. For a broad class of systems modelling one-step reversible chemical reactions, we show that blow-up in one component implies blow-up in all components at the same point in space and time. 1