Chemical Technology, Control and Management


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.

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