DIFFUSION-WAVE TYPE SOLUTIONS WITH TWO FRONTS TO A NONLINEAR DEGENERATE REACTION-DIFFUSION SYSTEM

Diffusion-wave type solutions are constructed and investigated for a nonlinear parabolic reaction-diffusion system. The statement of the problem in which mismatched zero fronts are set for different desired functions is considered for the first time. The existence and uniqueness theorem of solutions...

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Bibliographic Details
Published in:Journal of applied mechanics and technical physics 2022-12, Vol.63 (6), p.995-1004
Main Authors: Kazakov, A. L., Spevak, L. F.
Format: Article
Language:English
Subjects:
Analytic functions
Applications of Mathematics
Classical and Continuum Physics
Classical Mechanics
Collocation methods
Diffusion
Existence theorems
Fluid- and Aerodynamics
Iterative algorithms
Iterative methods
Mathematical Modeling and Industrial Mathematics
Mechanical Engineering
Physics
Physics and Astronomy
Radial basis function
Uniqueness theorems
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Summary:Diffusion-wave type solutions are constructed and investigated for a nonlinear parabolic reaction-diffusion system. The statement of the problem in which mismatched zero fronts are set for different desired functions is considered for the first time. The existence and uniqueness theorem of solutions in the form of series in a class of piecewise analytic functions is proven. It is proposed to construct the desired type of approximate solutions using a step-by-step iterative algorithm based on the collocation method and expansion in radial basis functions. Calculations are performed, and the results of these calculations are verified using the series segments. The behavior of the constructed solutions is numerically analyzed.
ISSN:0021-8944
1573-8620
DOI:10.1134/S0021894422060128