Abstract:
A family of exact solutions of an evolution equation describing the combustion process in a medium with a power-law temperature dependence of the source density is found. A formal asymptotics of the solution of the initial boundary value problem for the reaction-diffusion equation is constructed. The correctness of the partial sum of an asymptotic series is proved using the method of differential inequalities.
Citation:
A. A. Bykov, K. E. Ermakova, “Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order”, Zh. Vychisl. Mat. Mat. Fiz., 58:12 (2018), 2060–2073; Comput. Math. Math. Phys., 58:12 (2018), 1977–1988
\Bibitem{BykErm18}
\by A.~A.~Bykov, K.~E.~Ermakova
\paper Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 12
\pages 2060--2073
\mathnet{http://mi.mathnet.ru/zvmmf10805}
\crossref{https://doi.org/10.31857/S004446690003552-8}
\elib{https://elibrary.ru/item.asp?id=36759177}
\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 12
\pages 1977--1988
\crossref{https://doi.org/10.1134/S0965542518120084}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10805
https://www.mathnet.ru/eng/zvmmf/v58/i12/p2060
This publication is cited in the following 1 articles:
A. A. Bykov, K. E. Ermakova, “Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium”, Math. Models Comput. Simul., 12:3 (2020), 329–347