Solutions to a Nonlinear Degenerating Reaction- Diffusion System of the Type of Diffusion Waves with Two Fronts
A. L. Kazakov1, L. F. Spevak2
1Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033, Russia
2Gorkunov Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620049, Russia
Keywords: reaction-diffusion system, diffusion wave, existence and uniqueness theorem, power series, radial basis functions
Abstract
For a non-linear parabolic reaction-diffusion system, solutions of the diffusion wave type are constructed and investigated. For the first time, the formulation of the problem is considered, which involves the assignment of non-coinciding zero fronts for various desired functions. A theorem on the existence and uniqueness of solutions in the form of series in the class of piecewise analytic functions is proved. To construct approximate solutions of the desired type, a step-by-step iterative algorithm based on the collocation method and expansion in radial basis functions is proposed. Calculations were performed, for the verification of the results of which segments of the series were used. A numerical analysis of the behavior of the constructed solutions was carried out.
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