This chapter contains a general presentation of parabolic partial differential equations that
are used in biology: Lotka-Volterra systems and chemical or enzymatic reactions. These are …

We present a refined duality estimate for parabolic equations. This estimate entails new
results for systems of reaction-diffusion equations, including smoothness and exponential …

We consider systems of reaction–diffusion equations as gradient systems with respect to an
entropy functional and a dissipation metric given in terms of a so-called Onsager operator …

We prove global existence in time of weak solutions to a class of quadratic reaction-diffusion
systems for which a Lyapounov structure of L log L-entropy type holds. The approach relies …

The quantitative convergence to equilibrium for reaction-diffusion systems arising from
complex balanced chemical reaction networks with mass action kinetics is studied using the …

In the present work we introduce the notion of a renormalized solution for reaction–diffusion
systems with entropy-dissipating reactions. We establish the global existence of …

The global existence of classical solutions to reaction-diffusion systems in arbitrary space
dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly …

R.–Ce travail est consacré à l'étude de la régularité des solutions de certains
systèmes d'équations de réaction-diffusion. En particulier, nous montrons que les solutions …

We establish a weak–strong uniqueness principle for solutions to entropy-dissipating
reaction–diffusion equations: As long as a strong solution to the reaction–diffusion equation …

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion
systems modeling reversible chemical reactions under the detailed-balance condition. We …