On asymptotic stability of semi-linear distributed parameter dissipative systems

The concept of asymptotic stability is studied for a class of semi-linear distributed parameter dissipative systems with nonlinearity defined on a convex subset of the state space. This is achieved by using infinite-dimensional Banach state space description. Stability criteria are established, which are based on a weaker technical condition of the mm-dissipativity. These theoretical results are applied to a class of transport–reaction processes. Different types of nonlinearities are studied by adapting the criteria given in the early portions of the paper.