Affiliations: [a] Zentrum Mathematik, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany. E-mail: henneke@ma.tum.de | [b] Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria | [c] School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam. E-mail: quoc.tang@uni-graz.at
Abstract: The fast reaction limit of a volume–surface reaction–diffusion system is rigorously investigated. The system is motivated by proteins localisation in stem cell division. By using Ball’s energy equation method, we show that as the reaction rate constant goes to infinity, the solution of the original system converges to the solution of a heat equation with dynamical boundary condition. As a consequence, the dynamical boundary condition can be interpreted as a fast reaction limit of a volume–surface reaction–diffusion system.
Keywords: volume–surface reaction–diffusion systems, fast reaction limit, dynamical boundary condition, energy equation method, entropy method
