Investigation properties of solutions of a nonlinear system of equations with non homogeneous density and source

In this work the properties of the solution of self-similar and approximately self-similar solutions of equations for a reaction-diffusion system with double nonlinearity are investigated. The influence of the parameters of the reaction-diffusion system in the evolution process is investigated. Existence of parameter values for which the equation has a finite solution is proven. The system of equations considered in this work is based on many physical processes, for example, this system describes the reaction-diffusion process, thermal conductivity, polytrophic filtering of gas and liquid in a nonlinear medium with a source. A special property of this equation is its degeneration. And therefore, we investigated a weak solution, since in this case the solution to the problem may not exist in the classical sense. The main method for studying the problem under consideration is self-similar and approximately self-similar approaches. These approaches are intensively used to study the properties of solutions with a finite perturbation rate, the properties of solutions with exacerbation, and localization of solutions. For this, we used the nonlinear splitting method to construct a system of self-similar equations.

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