SIGEST

Abstract

Mixtures of several coexisting species (such as gases, gases and liquids, biological species, or reacting chemicals) typically are modeled by reaction-diffusion systems, i.e., systems of parabolic equations (the diffusion components of the process) coupled by nonlinear functions of all the reacting quantities. The SIGEST paper in this issue, "Blowup in Reaction-Diffusion Systems with Dissipation of Mass," by Michel Pierre and Didier Schmitt, which appeared originally in volume 28 of SIAM Journal on Mathematical Analysis, March 1997, considers the specific class of reaction-diffusion systems with two important properties that hold for many applications: nonnegativity of the solution is preserved over time, and total mass of the components is nonincreasing for all time.Using a combination of mathematical analysis and symbolic computation, the authors have devised a series of explicit counterexamples to global solvability for even the simplest system of 2 $\times$ 2 equations with good data. The paper not only shows that solutions do not exist in a variety of cases but also illustrates a very nice interplay among mathematical theory, symbolic computation, and numerical experimentation. We thank the authors for their contribution to SIAM Review.