The Global Solutions Problem for Population Quasi-Linear Equations of Parabolic Type

  • D. K. Muxamediyeva
Conference paper


Two classes of models have been investigated: the models of one population and the systems of competing populations. The algorithm of nonlinear splitting for the solution of the equations of multi-component competing systems of a biological population with a double nonlinearity is substantiated. Estimates are obtained for solving the Cauchy problem of multi-component competing systems of a biological population with a double nonlinearity, depending on the values of the parameters of the medium, the dimensionality of the space.


Global solution Parabolic equation Reaction-diffusion Biological population Self-similar solution Nonlinear model Nonlinear splitting method 


  1. 1.
    Marie J (1983) Nonlinear diffusion equations in biology. M., Mir, 397 pGoogle Scholar
  2. 2.
    Kolmogorov AN, Petrovsky IG, Piskunov NS (1937) Study of the diffusion equation connected with the increase in the amount of a substance and its application to a single biological problem. Bull Moscow State Univ 1(6):1–25Google Scholar
  3. 3.
    Aripov M (1988) Method of reference equations for solving nonlinear boundary value problems. Tashkent, Fan, 137 pGoogle Scholar
  4. 4.
    Мukhamedieva DK (2014) System of quasilinear equations of reaction-diffusion tasks of kolmogorov-fisher type biological population task in two-dimensional case. Int J Res Eng Technol 3(7):327–334. ISSN: 2319-1163 ISSN: 2321-7308 Impact Factor (JCC): 1.0174. Bangalore, IndiaGoogle Scholar
  5. 5.
    Mukhamedieva DK (2014) Self-similar solutions of the diffusion reaction system of a single problem of a biological population of the Kolmogorov-Fisher type. DAN RUz. – Tashkent (3):21–24Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • D. K. Muxamediyeva
    • 1
  1. 1.Scientific and Innovation Center of Information and Communication TechnologiesTashkentUzbekistan

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