A Reaction-Diffusion System with Nonconstant Diffusion Coefficients: Exact and Numerical Solutions

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dc.contributor.authorCherniha, Romanen_US
dc.contributor.authorKriukova, Galynaen_US
dc.date.accessioned2025-10-21T11:09:45Z
dc.date.available2025-10-21T11:09:45Z
dc.date.issued2025
dc.description.abstractA Lotka–Volterra-type system with porous diffusion, which can be used as an alternative model to the classical Lotka–Volterra system, is under study. Multiparameter families of exact solutions of the system in question are constructed and their properties are established. It is shown that the solutions obtained can satisfy the zero Neumann conditions, which are typical conditions for mathematical models describing real-world processes. It is proved that the system possesses two stable steady-state points provided its coefficients are correctly specified. In particular, this occurs when the system models the prey–predator interaction. The exact solutions are used for solving boundary-value problems. The analytical results are compared with numerical solutions of the same boundary-value problems but perturbed initial profiles. It is demonstrated that the numerical solutions coincide with the relevant exact solutions with high exactness in the case of sufficiently small perturbations of the initial profiles.en_US
dc.identifier.citationCherniha R. M. A Reaction-Diffusion System with Nonconstant Diffusion Coefficients: Exact and Numerical Solutions / Roman Cherniha, Galyna Kriukova // Axioms. - 2025. - Vol. 14, Issue 9. - Art. no. 655. - https://doi.org/10.3390/axioms14090655en_US
dc.identifier.issn2075-1680
dc.identifier.urihttps://doi.org/10.3390/axioms14090655
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/37274
dc.language.isoenen_US
dc.relation.sourceAxiomsen_US
dc.statusfirst publisheden_US
dc.subjectnonlinear reaction–diffusion systemen_US
dc.subjectLotka–Volterra systemen_US
dc.subjectmethod of additional generating conditionsen_US
dc.subjectexact solutionen_US
dc.subjectnumerical solutionen_US
dc.subjectarticleen_US
dc.titleA Reaction-Diffusion System with Nonconstant Diffusion Coefficients: Exact and Numerical Solutionsen_US
dc.typeArticleen_US
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