Stability preserving in reaction-diffusion systems

Reaction-diffusion systems are one of the most well-known partial differential equations used to model physical as well as chemical and biological phenomena. They consist of two parts describing different processes: the so called non-linear kinetic term which represents the driving forces and a linear diffusion term which is responsible for the spread of particles or individuals over a spatial domain. The non-linear part often depends on parameters which variation can influence the qualitative behaviour of the whole system. This paper investigates the question of how much the value of the system parameters can be changed such that the asymptotic stability of the stationary solution is maintained. For this purpose the framework of operator semigroup theory is studied and used.