|
This article is cited in 1 scientific paper (total in 1 paper)
Existence and asymptotic representation of the autowave solution of a system of equations
A. A. Melnikova, M. Chen Physical Faculty, Moscow State University, Moscow, Russia
Abstract:
A singularly perturbed parabolic system of nonlinear reaction-diffusion equations is studied. Systems of this class are used to simulate autowave processes in chemical kinetics, biophysics, and ecology. A detailed algorithm for constructing an asymptotic approximation of a travelling front solution is proposed. In addition, methods for constructing an upper and a lower solution based on the asymptotics are described. According to the method of differential inequalities, the existence of an upper and a lower solution guarantees the existence of a solution to the problem under consideration. These methods can be used for asymptotic analysis of model systems in applications. The results can also be used to develop and justify difference schemes for solving problems with moving fronts.
Key words:
system of reaction-diffusion equations, small parameter, internal transition layer, method of differential inequalities, contrast structures.
Received: 13.02.2017
Citation:
A. A. Melnikova, M. Chen, “Existence and asymptotic representation of the autowave solution of a system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018), 705–715; Comput. Math. Math. Phys., 58:5 (2018), 680–690
Linking options:
https://www.mathnet.ru/eng/zvmmf10731 https://www.mathnet.ru/eng/zvmmf/v58/i5/p705
|
|