Volume 11, no. 3Pages 85 - 102

Causal Relations in Support of Implicit Evolution Equations

N. Sauer, J. Banasiak, Wha-Suck Lee
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 infinite-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 differences 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 different way, is included in the survey.
Full text
implicit equations; empathy theory; semigroups.
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