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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 204, Pages 115–123
DOI: https://doi.org/10.36535/0233-6723-2022-204-115-123 (Mi into947) 		 
On sufficient conditions for the stability of a stationary solution and on one effect in diffusion models of oncological processes

M. V. Polovinkinaa, I. P. Polovinkinb

a Voronezh State University of Engineering Technologies
b Voronezh State University
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DOI: https://doi.org/10.36535/0233-6723-2022-204-115-123
Abstract: Sufficient conditions for the stability of the stationary solution in the population diffusion model of tumor growth and in the model of the immune response are established. An effect is revealed that is inherent only in the diffusion model, in contrast to the point model: the trivial solution may turn out to be stable depending on the size of the domain considered.
Keywords: system with distributed parameters, population diffusion model of tumor growth, immune response model, stability of stationary solution.
Document Type: Article
UDC: 517.957.7
MSC: 35Q92, 35B40, 92C50, 35J15
Language: Russian
Citation: M. V. Polovinkina, I. P. Polovinkin, “On sufficient conditions for the stability of a stationary solution and on one effect in diffusion models of oncological processes”, Proceedings of the Voronezh spring mathematical school  "Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI". Voronezh, May 3-9, 2020, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 204, VINITI, Moscow, 2022, 115–123
Citation in format AMSBIB
\Bibitem{PolPol22}
\by M.~V.~Polovinkina, I.~P.~Polovinkin
\paper On sufficient conditions for the stability of a stationary solution and on one effect in diffusion models of oncological processes
\inbook Proceedings of the Voronezh spring mathematical school 
"Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI".
Voronezh, May 3-9, 2020
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 204
\pages 115--123
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into947}
\crossref{https://doi.org/10.36535/0233-6723-2022-204-115-123}
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