Back
 JAMP  Vol.3 No.10 , October 2015
Qualitative Properties and Numerical Solution of the Kolmogorov-Fisher Type Biological Population Task with Double Nonlinear Diffusion
Abstract: In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.
Cite this paper: Muhamediyeva, D. (2015) Qualitative Properties and Numerical Solution of the Kolmogorov-Fisher Type Biological Population Task with Double Nonlinear Diffusion. Journal of Applied Mathematics and Physics, 3, 1249-1255. doi: 10.4236/jamp.2015.310153.
References

[1]   Aripov, M. (1988) Method Reference Equations for the Solution of Nonlinear Boundary Value Problems. Fan, Tashkent, 137.

[2]   Belotelov, N.V. and Lobanov, A.I. (1997) Population Model with Nonlinear Diffusion. Mathematic Modeling, 12, 43-56.

[3]   Volterra, V. (1976) The Mathematical Theory of the Struggle for Existence. Science, Moscow, 288.

[4]   Gause, G.F. (1934) About the Processes of Destruction of One Species by Another in the Populations of Ciliates. Zoological Journal, 1, 16-27.

[5]   Aripov, M. and Muhammadiev, J. (1999) Asymptotic Behaviour of Automodel Solutions for One System of Quasilinear Equations of Parabolic Type. France. Buletin Stiintific-Universitatea din Pitesti, Seria Matematica si Informatica, 19-40.

[6]   Aripov, M.M. and Muhamediyeva, D.K. (2013) 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, 2, 281-286.

[7]   Aripov, M.M. and Muhamedieva, D.K. (2013) Approaches to the Solution of One Problem of Biological Populations. Issues of Computational and Applied Mathematics, 129, 22-31.

[8]   Murray, D.J. (1983) Nonlinear Diffusion Equations in Biology. Mir, Moscow, 397.

[9]   Huashui, Z. (2010) The Asymptotic Behavior of Solutions for a Class of Doubly Degenerate Nonlinear Parabolic Equations. Journal of Mathematical Analysis and Applications, 370, 1-10.
http://dx.doi.org/10.1016/j.jmaa.2010.05.003

 
 
Top