Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium
A. A. Bykov, K. E. Ermakova
Lomonosov Moscow State University, Faculty of Physics, Department of Mathematics
A description is given of contrasting structures arising from the simulation of reaction – diffusion processes in an inhomogeneous medium with a power dependence of the source density on the concentration in the vicinity of the roots. The results obtained earlier for a homogeneous medium are generalized to the case of an inhomogeneous medium, and sufficient conditions for the existence of a solution of the type of contrast structure are strictly substantiated. The exponent of the root function of the right-hand side, in contrast to previously known results, is assumed to be non-integer, including irrational. It is shown that the front (relative to the direction of movement) part of the front is an exponential function, the rear part of the front is a power function, and this is a fundamentally new, previously unknown result. The family of exact solutions of the evolution equation is found. The formal asymptotics of the solution of the initial-boundary value problem for the reaction-diffusion equation is constructed. The substantiation of the correctness of the partial sum of an asymptotic series using the method of differential inequalities is given.
nonlinear differential equations, asymptotic methods, contrast structure, differential inequalities.
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A. A. Bykov, K. E. Ermakova, “Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium”, Matem. Mod., 31:9 (2019), 101–130
Citation in format AMSBIB
\by A.~A.~Bykov, K.~E.~Ermakova
\paper Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium
\jour Matem. Mod.
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