Abstract:
In the article the mathematical model representing one class of evolution equations in quasi-Banach spaces is studied. A theorem on the unique solvability of the Cauchy problem is stated. The conditions for the phase space existence are presented. We also give the conditions for exponential dichotomies of solutions. Based on the theoretical results there was developed an algorithm for the numerical solution of the problem. The algorithm is implemented in Maple. The article includes description of the algorithm which is illustrated by variety of model examples showing the work of the developed program and represent the main properties of solutions.
Citation:
J. K. T. Al-Isawi, A. A. Zamyshlyaeva, “Computational experiment for one class of evolution mathematical models in quasi-Sobolev spaces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:4 (2016), 141–147
\Bibitem{Al-Zam16}
\by J.~K.~T.~Al-Isawi, A.~A.~Zamyshlyaeva
\paper Computational experiment for one class of evolution mathematical models in quasi-Sobolev spaces
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2016
\vol 9
\issue 4
\pages 141--147
\mathnet{http://mi.mathnet.ru/vyuru351}
\crossref{https://doi.org/10.14529/mmp160413}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000390883900013}
\elib{https://elibrary.ru/item.asp?id=27318775}
Linking options:
https://www.mathnet.ru/eng/vyuru351
https://www.mathnet.ru/eng/vyuru/v9/i4/p141
This publication is cited in the following 3 articles:
O. V. Gavrilova, “Chislennoe issledovanie odnoznachnoi razreshimosti zadachi Shouoltera – Sidorova dlya matematicheskoi modeli rasprostraneniya nervnykh impulsov v membranoi obolochke”, J. Comp. Eng. Math., 8:3 (2021), 32–48
J. K. T. Al-Isawi, “Computational experiments for one class of mathematical models in thermodynamics and hydrodynamics”, J. Comp. Eng. Math., 4:1 (2017), 16–26
K. V. Vasyuchkova, N. A. Manakova, G. A. Sviridyuk, “Some mathematical models with a relatively bounded operator and additive “white noise” in spaces of sequences”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:4 (2017), 5–14
Citation in format AMSBIB
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