Abstract:
This is a brief exposition of dynamic systems approaches that form the basis for linear
implicit evolution equations with some indication of interesting applications. Examples in
in nite-dimensional dissipative systems and stochastic processes illustrate the fundamental
notions underlying the use of double families of evolution equations intertwined by the
empathy relation. Kisy nski's equivalent formulation of the Hille Yosida theorem highlights
the essential di erences between semigroup theory and the theory of empathy. The notion
of K-bounded semigroups, a more direct approach to implicit equations, and related to
empathy in a di erent way, is included in the survey.
