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Chemical Technology, Control and Management

Abstract

The models of two competing populations with double nonlinear diffusion and three types of functional dependencies are considered. The first dependence corresponds to the Malthusian type, the second to the Verhühlst type (logistic population), and the third to Olli-type populations. A common element of this kind of description is the presence of a linear source. Nonlinear sinks are also present in descriptions of populations of the Verhulst and Ollie type. Suitable initial approximations for a rapidly converging iterative process are proposed. Based on a self-similar analysis and comparison of the solutions of the Cauchy problem in the domain for an equation with double nonlinearity, the properties of the solution of the self-similar equation are investigated. The above properties are established on the basis of the solution comparison theorem, and the asymptotics of self-similar solutions are obtained.

First Page

45

Last Page

50

References

  1. Ansgar Jungel. Cross-diffusion systems with entropy structure. Proceedings of EQUADIFF. 2017. – pp. 1–10.
  2. Aripov Mersaid. The Fujita and Secondary Type Critical Exponents in Nonlinear Parabolic Equations and Systems. Differential Equations and Dynamical Systems. 2018. –pp. 9-25.
  3. Sh.A.Sadullaeva, M.B.Khojimurodova. Properties of Solutions of the Cauchy Problem for Degenerate Nonlinear Cross Systems with Convective Transfer and Absorption. Algebra, complex analysis and Pluripotential theory.2 USUZCAMP, Urgench, Uzbekistan, August 8–12, 2017. –pp 183-190.
  4. Murray J.D. Mathematical Biology. I. An Introduction (Third Edition). – N.Y., Berlin, Heidelberg: Springer Verlag, 2001. – 551 p.
  5. M. Aripov. «Approximate Self-similar Approach tu Solve Quasilinear Parabolic Equation» Experimentation, Modeling and Computation in Flow Turbulence and Combustion. vol. 2. 1997. – pp. 19- 26.
  6. Aripov M. Metod e`talonny'h uravneniy dlya resheniya nelineyny'h kraevy'h zadach. -T.: Fan, 1988, - 137 s.
  7. Belotelov N.V., Lobanov A.I. Populyacionny'e modeli s nelineynoy diffuziey. // Matematicheskoe modelirovanie. -M.; 1997, №12, -s. 43-56.
  8. V. Vol'terra. Matematicheskaya teoriya bor'by' za susch'estvovanie -M.: Nauka, 1976, - 288 s.
  9. Gauze G.F. O processah unichtojeniya odnogo vida drugim v populyaciyah infuzoriy // Zoologicheskiy jurnal, 1934, t.13, №1.
  10. Aripov M., Muhammadiev J. Asymptotic behaviour of automodel solutions for one system of quasilinear equations of parabolic type. Buletin Stiintific-Universitate a din Pitesti, Seria Matematicasi Informatica. N 3. 1999. –pp. 19-40.
  11. Aripov M.M. Muhamediyeva D.K. To the numerical modeling of self-similar solutions of reaction-diffusion system of the one task of biological population of Kolmogorov-Fisher type. International Journal of Engineering and Technology. Vol-02, Iss-11, Nov-2013. India. 2013.
  12. Aripov M.M. Muhamedieva D.K. Podhody' k resheniyu odnoy zadachi biologicheskoy populyacii. Voprosy' vy'chislitel'noy i prikladnoy matematiki. -Tashkent. 2013. Vy'p.129. -S.22-31.
  13. Muxamediyeva D.K. Properties of self similar solutions of reaction-diffusion systems of quasilinear equations // International Journal of Mechanical and production engineering research and development (IJMPERD) ISSN(P): 2249-6890; ISSN(E): 2249-8001 Vol. 8, Issue 2, USA. 2018, 555-565 pp. Impact Factor (JCC): 6.8765. DOI:10.24247/ijmperdapr201864.
  14. Muhamediyeva D.K. Solving of the Task of Kolmogorov-Fisher Type Biological Population in the Regime with Aggravation // International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 6 (2018) pp. 4291-4298.
  15. Muhamediyeva D.K. Some exact and numerical solution of the problem of Kolmogorov-Fisher type biological population task with double nonlinear diffusion //International Journal of Research in Engineering and Technology, Vol.6, №9, 2017, p.37-45.
  16. Mukhamediyeva D.K. Population model with cross-diffusion with double nonlinearity //International Journal of Management, Information Technology and Engineering, Vol. 5, № 9, 2017, p.43-52.
  17. Muhamediyeva D. K. Invariance properties and estimating task solution of biological population in the two-dimensional case//International Journal of Applied Mathematics & Statistical Sciences (IJAMSS) ISSN(P): 2319-3972; ISSN(E): 2319-3980 Vol. 6, Issue 6, Oct – Nov 2017. – pp 1-8.

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