# Exact Solutions of Equations of a Nonstationary Front with Equilibrium Points of a Fractional Order

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### 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.

## Keywords:

nonlinear differential equations asymptotic methods contrast structure differential inequalities## Notes

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