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On the stability of stationary solutions in diffusion models of oncological processes

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Abstract

We prove a sufficient condition for the stability of a stationary solution to a system of nonlinear partial differential equations of the diffusion model describing the growth of malignant tumors. We also numerically simulate stable and unstable scenarios involving the interaction between tumor and immune cells.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Guelma University, 24000, Guelma, Algeria

    A. Debbouche

  2. Department of higher mathematics and information technologies, Voronezh State University of Engineering Technologies, Revolution Av., 19, Voronezh, Russian Federation

    M. V. Polovinkina

  3. Department of mathematical and applied analysis, Voronezh State University, Universitetskaya pl.,1, Voronezh, Russian Federation

    I. P. Polovinkin

  4. Center on Differential Equations and Applications, Belgorod State National Research University, Belgorod, Russian Federation

    I. P. Polovinkin

  5. Department of Biosystems Engineering, University of São Paulo, Pirassununga campus, Av. Duque de Caxias Norte 225, Pirassununga, SP, 13635-900, Brazil

    C. A. Valentim Jr.

  6. Systems Dynamics Group/Department of Biosystems Engineering, University of São Paulo, Pirassununga campus, Av. Duque de Caxias Norte 225, Pirassununga, SP, 13635-900, Brazil

    S. A. David

Authors
  1. A. Debbouche
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  2. M. V. Polovinkina
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  3. I. P. Polovinkin
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  4. C. A. Valentim Jr.
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  5. S. A. David
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Correspondence to A. Debbouche.

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Debbouche, A., Polovinkina, M.V., Polovinkin, I.P. et al. On the stability of stationary solutions in diffusion models of oncological processes. Eur. Phys. J. Plus 136, 131 (2021). https://doi.org/10.1140/epjp/s13360-020-01070-8

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-01070-8

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