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Matem. Mod., 2007, Volume 19, Number 6, Pages 31–42 (Mi mm977)  

This article is cited in 1 scientific paper (total in 1 paper)

Fisher type waves in a model of invasive tumor growth

A. V. Kolobov, V. V. Gubernov, A. A. Polezhaev

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: A mathematical model for the invasive tumor growth which includes nutrient distribution in tissue is developed. This model adequately describes constant rate of the tumor linear size growth with time and the formation of necrotic region in the tumor interior, observed in experiments. The existence of autowave solutions is demonstrated and their properties are investigated. The results are compared with the properties of the Kolmogorov–Petrovskii–Piskunov and Fisher equations. The perspective of further investigation and development of the model for studying glioma is discussed.

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Received: 27.06.2006

Citation: A. V. Kolobov, V. V. Gubernov, A. A. Polezhaev, “Fisher type waves in a model of invasive tumor growth”, Matem. Mod., 19:6 (2007), 31–42

Citation in format AMSBIB
\Bibitem{KolGubPol07}
\by A.~V.~Kolobov, V.~V.~Gubernov, A.~A.~Polezhaev
\paper Fisher type waves in a~model of invasive tumor growth
\jour Matem. Mod.
\yr 2007
\vol 19
\issue 6
\pages 31--42
\mathnet{http://mi.mathnet.ru/mm977}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2423987}
\zmath{https://zbmath.org/?q=an:1137.92327}


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    This publication is cited in the following articles:
    1. N. A. Kudryashov, K. E. Shilnikov, “Numerical modeling of the cellular necrosis front localization effect during cutaneous cryosurgery”, Math. Models Comput. Simul., 8:6 (2016), 680–688  mathnet  crossref  elib
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