Appears in collection : 2017 - T2 - Stochastic Dynamics out of Equilibrium

Chemical reaction networks appear in many industrial devices and natural processes (combustion, photosynthesis, etc. ). When the spatial structure is not taken into account, they give rise to complex system of ODEs with polynomial terms, and a lot of results were obtained lately in the study of the large time behavior for the solutions of those systems. When the chemical species are supposed to be traces in a solvent, they are diffusing (each with its diffusion rate), so that their concentrations are solution to a system of reaction-diffusion with polynomial reaction rates. The specificity of such systems is, at least for a large class of them (called systems with balanced equilibria) the existence of a Lyapunov functional related to the physical entropy. Recently, the systems of reaction-diffusion coming out of chemical networks with balanced equilibria have attracted a lot of attention. The study of existence of weak and strong solutions to those systems uses a lot of subtle tools of analysis: renormalized solutions, duality methods, etc. Their large time behavior is also an interesting issue. It is possible to develop entropy methods and convexity arguments which enable to show convergence to equilibrium for some systems, but many interesting systems are still puzzling. In this series of lectures, we shall present (using specific examples) the main features of reaction-diffusion systems related to chemical networks, and explain how to get typical existence results as well as large time behavior results.