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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2018, Volume 11, Issue 3, Pages 85–102 (Mi vyuru446)  

Mathematical Modelling

Causal relations in support of implicit evolution equations

N. Sauer, J. Banasiak, W.-S. Lee

University of Pretoria, South Africa

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 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.

DOI: https://doi.org/10.14529/mmp180307

Full text: PDF file (362 kB)
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Document Type: Article
UDC: 517.9+519.21+517.958
MSC: 34K32, 47D06, 47D07
Received: 02.07.2018
Language: English

Citation: N. Sauer, J. Banasiak, W.-S. Lee, “Causal relations in support of implicit evolution equations”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 11:3 (2018), 85–102

Citation in format AMSBIB
\Bibitem{SauBanLee18}
\by N.~Sauer, J.~Banasiak, W.-S.~Lee
\paper Causal relations in support of implicit evolution equations
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2018
\vol 11
\issue 3
\pages 85--102
\mathnet{http://mi.mathnet.ru/vyuru446}
\crossref{https://doi.org/10.14529/mmp180307}


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