For those interested in this topic, we are organizing a minisymposium at the European Solid Mechanics Conference (sponsored by EUROMECH) in Bologna, in 2018, see session 9.2:
http://www.esmc2018.org/drupal8/node/9
Some examples are:
Reaction diffusion and Brinkman flow to model chemical reactions and the motion of a contaminated viscous fluid:
http://www.sciencedirect.com/science/article/pii/S0021999117303807
https://www.google.it/url?sa=t&source=web&rct=j&url=https://hal.archive…
Degradation of polymers (temperature, moisture and chemical reactions):
http://www.sciencedirect.com/science/article/pii/S0927024817300673?via%…
Other well known applications regard biological systems, such as electrophysiology of the hearth, and brain growth models based on Turing instabilities.
Due to the different dynamics and time scales of the fields involved, novel time integration schemes have been developed.
We encourage participation from any field of mechanics, with original contributions on mathematical modelling, numerical methods, physical evidences related to the exploitation of reaction diffusion systems in mechanics.
For reaction-diffusion and
For reaction-diffusion and mechanics of cardiac myocytes, including also for the first time a computational model for contact interactions between myocytes and adhesion, see:
https://arxiv.org/abs/1707.00920