Derivation of effective interface conditions for reaction-diffusion equations

We address the derivation of effective interface conditions for reaction-diffusion systems. The considered system is defined in a domain containing a thin layer that shrinks to the interface when its thickness ε tends to zero. The evolution of the system can be written in the form of an energy balance involving an energy and a dissipation functional. Using the Mosco convergence of the dual of the dissipation functional for ε → 0 it is possible to do a limit passage in the energy balance and obtain a limit system that describes the evolution on the interface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)