Geodesic
Causal relations in support of implicit evolution equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 85-102

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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. Kisyński'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.
Keywords: implicit equations; empathy theory; semigroups. 
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N. Sauer; J. Banasiak; W.-S. Lee. Causal relations in support of implicit evolution equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 85-102. http://geodesic.mathdoc.fr/item/VYURU_2018_11_3_a6/