EXACT AND APPROXIMATE SOLUTIONS OF A DEGENERATE REACTION–DIFFUSION SYSTEM

We consider the problem of constructing exact solutions to a system of two coupled nonlinear parabolic reaction–diffusion equations. We study solutions in the form of diffusion waves propagating over zero background with a finite speed. The theorem on the construction of exact solutions by reducing...

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Bibliographic Details
Published in:Journal of applied mechanics and technical physics 2021-07, Vol.62 (4), p.673-683
Main Authors: Kazakov, A. L., Spevak, L. F.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Cauchy problems
Classical and Continuum Physics
Classical Mechanics
Differential equations
Diffusion rate
Diffusion waves
Exact solutions
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mechanical Engineering
Numerical analysis
Ordinary differential equations
Physics
Physics and Astronomy
Radial basis function
Reaction-diffusion equations
Wave propagation
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Summary:We consider the problem of constructing exact solutions to a system of two coupled nonlinear parabolic reaction–diffusion equations. We study solutions in the form of diffusion waves propagating over zero background with a finite speed. The theorem on the construction of exact solutions by reducing to the Cauchy problem for a system of ordinary differential equations (ODEs) is proved. A time-step numerical technique for solving the reaction-diffusion system using radial basis function expansion is proposed. The same technique is used to solve the systems of ordinary differential equations defining exact solutions to the reaction–diffusion system. Numerical analysis and estimation of the accuracy of solutions to the system of ODEs are carried out. These solutions are used to verify the obtained time-step solutions of the original system..
ISSN:0021-8944
1573-8620
DOI:10.1134/S0021894421040179